Teses / dissertações sobre o tema "Copules (mathématiques)"
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Lmoudden, Aziz. "Une généralisation de la copule de Khoudraji. Copules engendrées par des fonctions complètement monotones". Thesis, Université Laval, 2011. http://www.theses.ulaval.ca/2011/28122/28122.pdf.
Texto completo da fonteRomdhani, Hela. "Mesures d'association pour des modèles de copules multidimensionnelles". Thesis, Université Laval, 2013. http://www.theses.ulaval.ca/2013/29875/29875.pdf.
Texto completo da fonteIn this thesis we are interested in measuring the dependence under copula models. We deal with three problems: the measure of association in the bivariate case in the presence of lower detection limits, the measure of association for clustered data and the measure of association for two-level hierarchical data. The first problem, independent of the other two, deals with the measure of association between two variables subject to fixed left censoring due to the presence of lower detection limits. We define a conditional version of Kendall’s tau to measure the association between such variables. We provide a nonparametric estimator of this measure and study its asymptotic properties. We then assume an Archimedean copula model and deduce an estimator for the copula’s Kendall’s tau. A goodness-of-fit test for the assumed copula is developed. The second problem deals with the measure of intra-class association for clustered data such that observations within each group are exchangeable. For this, we introduce an exchangeable version of Kendall’s tau as a measure of intra-class dependance and provide a nonparametric estimator for this measure. Its asymptotic properties are investigated under a multivariate exchangeable copula model. We derive an estimator of the intra-class correlation coefficient for data drawn from an elliptical distribution. The asymptotic properties of this estimator are investigated under a generalized oneway ANOVA model. Finally, we develop an intra-class independence test based on Kendall’s tau. The third problem is an extension of the second to the case of hierarchical data with a set of subgroups nested into groups, such that the units within each subgroup are exchangeable and the subgroups belonging to the same group are themselves exchangeable. We define two association measures based on the exchangeable Kendall’s tau and propose nonparametric estimators for these measures. We investigate their asymptotic properties under hierarchical copula models satisfying some properties of partial exchangeability. For data drawn from meta-elliptical hierarchical copulas we deduce estimators for the intra-class correlation coefficients associated to groups and subgroups respectively. We also develop procedures for testing the effects of groups and subgroups.
Totouom, Tangho Daniel. "Copules dynamiques : applications en finance & en économie". Paris, ENMP, 2007. https://pastel.archives-ouvertes.fr/pastel-00003260.
Texto completo da fonteIn this thesis, we show that with the growth of credit derivatives markets, new products are continually being created and market liquidity is increasing. After reviewing these products starting out from the credit default swap, CDS, and describing their evolution since their inception in the early 90s, we demonstrate that this development has been market driven, with the mathematical models used for pricing lagging behind. As the market developed, the weak points of the models became apparent and improved models had to be developed. In October 2003 when the work on this thesis started, CDOs (Collateralised Debt Obligations) were becoming standard products. A new generation of products which we will refer to as third generation credit derivatives were starting to come on line: these include forward-starting CDS, forward-starting CDOs, options on CDOs, CPDO (in full) and so forth. In contrast to early products, these derivatives require a dynamic model of the evolution of the “correlation” between the names over time, something which base correlation was not designed to do. Our objective was to develop a family of multivariate copula processes with different types of upper and lower tail dependence so as to be able to reproduce the correlation smiles/skews observed in credit derivatives in practice. We chose to work with a dynamic version of Archimedean copulas because unlike many other copulas found in the literature, they are mathematically consistent multivariate models. Chapter 2 presents two different approaches for developing these processes. The first model developed is a non-additive jump process based on a background gamma process; the second approach is based on time changed spectrally positive Levy process. The first approach is very convenient for simulations; the second approach is based on additive building blocks and hence is a more general. Two applications of these models to credit risk derivatives were carried out. The first one on pricing synthetic CDOs at different maturities (Chapter 5) was presented at the 5th Annual Advances in Econometrics Conference in Baton Rouge, Louisiane, November 3-5 2006 and has been submitted for publication. The second one which presents a comparison of the pricing given by these dynamic copulas with five well-known copula models, has been submitted to the Journal of Derivatives (see Chapter 6). Having tested the basic dynamic copula models in a credit derivative context, we went on to combine this framework with matrix migration approach (Chapter 3). In order to market structured credit derivatives, banks have to get them rated by rating agencies such as S&P, Moody’s and Fitch. A key question is the evolution of the rating over time (i. E. Its migration). As the latest innovations in the credit derivatives markets such as Constant Proportion Debt Obligation (CPDO) require being able to model credit migration and correlation in order to handle substitutions on the index during the roll, we propose a model for the joint dynamics of credit ratings of several firms. We then proposed a mathematical framework were individual credit ratings are modelled by a continuous time Markov chain, and their joint dynamics are modelled using a copula process. Copulas allow us to incorporate our knowledge of single name credit migration processes, into a multivariate framework. This is further extended with the multi-factor and time changed approach. A multifactor approach is developed within the new formulated dynamic copula processes, and a time changed Levy process is used to introduce dependency on spread dynamics
Bourdeau-Brien, Michaël. "Les copules en finance : analyse qualitative et quantitative de l'expansion de cette théorie". Master's thesis, Université Laval, 2007. http://hdl.handle.net/20.500.11794/19266.
Texto completo da fonteDesbois-Bédard, Laurence. "Génération de données synthétiques pour des variables continues : étude de différentes méthodes utilisant les copules". Master's thesis, Université Laval, 2017. http://hdl.handle.net/20.500.11794/27748.
Texto completo da fonteStatistical agencies face a growing demand for releasing microdata to the public. To this end, many techniques have been proposed for publishing microdata while providing confidentiality : synthetic data generation in particular. This thesis focuses on such technique by presenting two existing methods, GAPD and C-GADP, as well as suggesting one based on vine copula models. GADP assumes that the variables of original and synthetic data are normally distributed, while C-GADP assumes that they have a normal copula distribution. Vine copula models are proposed due to their flexibility. These three methods are then assessed according to utility and risk. Data utility depends on maintaining certain similarities between the original and confidential data, while risk can be observed in two types : reidentification and inference. This work will focus on the utility examined with different analysis-specific measures, a global measure based on propensity scores and the risk of inference evaluated with a distance-based prediction.
Ben, Ghorbal Noomen. "Étude de certaines mesures d'association multivariées et d'un test de dépendance extrémale fondés sur les rangs". Thesis, Université Laval, 2010. http://www.theses.ulaval.ca/2010/27602/27602.pdf.
Texto completo da fonteMarri, Fouad. "Évaluation des mesures de ruine dans le cadre de modèles avancés de risque". Thesis, Université Laval, 2009. http://www.theses.ulaval.ca/2009/26001/26001.pdf.
Texto completo da fonteCuberos, Andres. "Modélisation de la dépendance et estimation du risque agrégé". Thesis, Lyon 1, 2015. http://www.theses.fr/2015LYO10321/document.
Texto completo da fonteThis thesis comprises three essays on estimation methods for the dependence between risks and its aggregation. In the first essay we propose a new method to estimate high level quantiles of sums of risks. It is based on the estimation of the ratio between the VaR (or TVaR) of the sum and the VaR (or TVaR) of the maximum of the risks. We use results on regularly varying functions. We compare the efficiency of our method with classical ones, on several models. Our method gives good results when approximating the VaR or TVaR in high levels on strongly dependent risks where at least one of the risks is heavy tailed. In the second essay we propose an estimation procedure for the distribution of an aggregated risk based on the checkerboard copula. It allows to get good estimations from a (quite) small sample of the multivariate law and a full knowledge of the marginal laws. This situation is realistic for many applications. Estimations may be improved by including in the checkerboard copula some additional information (on the law of a sub-vector or on extreme probabilities). Our approach is illustrated by numerical examples. In the third essay we propose a kernel based estimator for the spectral measure density of a bivariate distribution with regular variation. An extension of our method allows to estimate discrete spectral measures. Some convergence properties are obtained
Chicheportiche, Rémy. "Dépendances non linéaires en finance". Phd thesis, Ecole Centrale Paris, 2013. http://tel.archives-ouvertes.fr/tel-01003349.
Texto completo da fonteVeilleux, Dery. "Modèles de dépendance avec copule Archimédienne : fondements basés sur la construction par mélange, méthodes de calcul et applications". Master's thesis, Université Laval, 2018. http://hdl.handle.net/20.500.11794/33039.
Texto completo da fonteThe law of large numbers, which states that statistical characteristics of a random sample will converge to the characteristics of the whole population, is the foundation of the insurance industry. Insurance companies rely on this principle to evaluate the risk of insured events. However, when we introduce dependencies between each component of the random sample, it may drastically affect the overall risk profile of the sample in comparison to the whole population. This is why it is essential to consider the effect of dependency when aggregating insurance risks from which stems the interest given to dependence modeling in actuarial science. In this thesis, we study dependence modeling in a portfolio of risks for which a mixture random variable (rv) introduces dependency. After introducing the use of exponential mixtures in actuarial risk modeling, we show how this mixture construction can define Archimedean copulas, a powerful tool for dependence modeling. First, we demonstrate how an Archimedean copula constructed via a continuous mixture can be approximated with a copula constructed by discrete mixture. Then, we derive explicit expressions for a few quantities related to the aggregated risk. The common mixture representation of Archimedean copulas is then at the basis of a computational strategy proposed to compute the distribution of the sum of risks in a general setup. Such results are then used to investigate risk models with respect to aggregation, capital allocation and ruin problems. Finally, we discuss an extension to nested Archimedean copulas, a general case of dependency via common mixture including different levels of dependency.
Résumé en espagnol
Toupin, Marie-Hélène. "La copule khi-carré et son utilisation en statistique spatiale et pour la modélisation de données multidimensionnelles". Doctoral thesis, Université Laval, 2017. http://hdl.handle.net/20.500.11794/27977.
Texto completo da fonteThis thesis studies the properties of the family of chi-square copulas. This is a generalization of the multidimensional normal copulas obtained by squaring the components of normal random vector. These copulas are indexed by a correlation matrix and by a shape parameter. This thesis shows how this family can be used to perform spatial interpolation and to model multidimensional data. First, the usefulness of this class of dependence structures is demonstrated with an application in spatial statistics. An important problem in that context is to predict the value of a stationary random field at a position where it has not been observed. This thesis shows how to construct such predictions using spatial models based on copulas. One focusses on the use of the family of chi-square copulas in that context. One must first assumes that the correlation matrix has a standard parametric form, such as that of Matérn, indexed by an unknown parameter associated with the force of the spatial association. This parameter is first estimated using a composite pseudo-likelihood constructed from the bivariate distributions of the observed data. Then, a spatial interpolation method using the ranks of the observations is suggested to approximate the best prediction of the random field at an unobserved position under a chi-square copula. In a second work, the fundamental properties of the chi-square copulas are studied in detail. This family allows a lot of flexibility to model multidimensional data. In the bivariate case, this family is adapted to symmetric and asymmetric dependence structures. In larger dimensions, the shape parameter controls the degree of radial asymmetry of the two-dimensional marginal distributions. Parameter estimation procedures of the correlation matrix and of the shape parameter are compared under independent and identically distributed repetitions. Finally, the formulas of the conditional expectation for the best prediction in a spatial context are established. Goodness-of-fit tests for the family of chi-square copulas are then developed. These new tests can be applied to data in any dimension. These procedures are based on two association measures based on the ranks of the observations, which avoids having to specify the marginal distributions. It is shown that the joint behavior of these two measures is asymptotically normal. The efficiency of the new goodness-of-fit procedures is demonstrated through a simulation study and is compared to a classical goodness-of-fit test based on the empirical copula.
Chatelain, Simon. "Modélisation de la dépendance entre pré-extrêmes". Thesis, Lyon, 2019. http://www.theses.fr/2019LYSE1267.
Texto completo da fonteIn various applications in environmental sciences, finance, insurance or risk management, joint extremal behavior between random variables is of particular interest. For example, this plays a central role in assessing risks of natural disasters. Misspecification of the dependence between random variables can lead to substantial underestimation of risk, especially at extreme levels. This thesis develops inference techniques for Archimax copulas. These copula models can account for any type of asymptotic dependence between extremes and at the same time capture joint risks at medium levels. An Archimax copula is characterized by two functional parameters, the stable tail dependence function (stdf), and the Archimedean generator which acts as a distortion of the extreme-value dependence model. Conditions under which the generator and the stdf are identifiable are derived so that a semiparametric approach for inference can be developed. Two nonparametric estimators of the stdf and a moment-based estimator of the generator, which assumes that the latter belongs to a parametric family, are proposed. The asymptotic behavior of the estimators is then established under broad regularity conditions; performance in small samples is assessed through a comprehensive simulation study. In the second part of the thesis, Archimax copulas are generalized to a clustered constructions in order to bring in more flexibility, which is needed in practical applications. The extremal behavior of this new dependence model is derived herein. Finally, the methodology proposed herein is illustrated on precipitation data. First, a trivariate Archimax copula is used to analyze monthly rainfall maxima at three stations in French Brittany. The model is seen to fit the data very well, both in the lower and in the upper tail. The nonparametric estimator of the stdf reveals asymmetric extremal dependence between the stations, which reflects heavy precipitation patterns in the area. An application of the clustered Archimax model to a precipitation dataset containing 155 stations is then presented, where groups of asymptotically dependent stations are determined via a specifically tailored clustering algorithm. Finally, possible ways to model inter cluster dependence are discussed
Beaudoin, David. "Estimation de la dépendance et choix de modèles pour des données bivariées sujettes à censure et à troncation". Thesis, Université Laval, 2007. http://www.theses.ulaval.ca/2007/24621/24621.pdf.
Texto completo da fonteMtalai, Itre. "Modélisation de la dépendance à l'aide des mélanges communs et applications en actuariat". Doctoral thesis, Université Laval, 2018. http://hdl.handle.net/20.500.11794/32983.
Texto completo da fonteLa modélisation de la dépendance entre les risques pour un portefeuille d’une assurance ou d’une entité financière est devenue de plus en plus importante pour la solvabilité des institutions financières et l’examen de solvabilité dynamique et l’analyse financière dynamique des compagnies d’assurance. L’hypothèse d’indépendance entre les risques est parfois réaliste et facilite l’évaluation, l’agrégation et l’allocation des risques. Cependant, dans la majorité des cas, les risques individuels sont influencés par un ou plusieurs facteurs communs, tels que l’environnement économique, les régions géographiques ou les conditions climatiques et il est donc moins réaliste, voire dangereux, de supposer l’indépendance entre les risques d’un même portefeuille. Dans la littérature, un tel cas peut être modélisé par des modèles avec mélange commun. Ces modèles ont de nombreuses applications en assurance et en finance. L’objectif de cette thèse est donc d’explorer les modèles de dépendance construits à l’aide des mélanges communs et de faire sortir, à l’aide de plusieurs applications, la dangerosité de considérer l’indépendance entre les risques au sein d’un portefeuille. En particulier, la focalisation est mise sur un modèle souvent considéré pour modéliser le montant de sinistres, notamment la loi exponentielle mélange. Cette thèse considère les modèles de risque basés sur la loi exponentielle mélange. Le premier chapitre constitue une introduction générale aux modèles avec mélanges communs et introduit les notions qui seront utilisées dans les autres chapitres. Dans le deuxième chapitre, nous considérons un portefeuille de risques représentés par un vecteur de variables aléatoires dont la fonction de répartition conjointe est définie par une copule Archimédienne ou une copule Archimédienne imbriquée. Nous examinons le calcul de la fonction de répartition de la somme ou une variété de fonctions de ces variables aléatoires. En nous basant sur la méthodologie computationnelle présentée dans ce chapitre, nous examinons plusieurs problèmes reliés à différents modèles de risque en actuariat, tels que l’agrégation et l’allocation du capital. De plus, en utilisant une telle structure de dépendance avec des marginales spécifiques, nous obtenons des expressions explicites pour plusieurs quantités relatives au risque agrégé telles que sa fonction de masse de probabilité, sa fonction de répartition, sa TVaR, etc. L’échangeabilité des copules Archimédiennes implique que toutes les marginales sont égales. Afin de généraliser les copules Archimédiennes pour permettre les asymétries, plusieurs chercheurs utilisent une structure hiérarchique obtenue en imbriquant plusieurs copules Archimédiennes. Toutefois, il est difficile de valider la condition d’imbrication permettant d’assurer que la structure résultante est une copule, lorsque les copules impliquées appartiennent à des familles Archimédiennes différentes. Afin de remédier à ce problème, nous présentons, au troisième chapitre, une nouvelle méthode d’imbrication basée sur la construction des lois composées multivariées exponentielles mélange. En introduisant plusieurs paramètres, un large spectre de structures de dépendance peut être couvert par cette nouvelle construction, ce qui semble être très intéressant pour des applications pratiques. Des algorithmes efficients de simulation et d’agrégation sont également présentés. En nous inspirant à la fois des chapitres 2 et 3, nous proposons et examinons en détail au quatrième chapitre une nouvelle extension au modèle collectif de risque en supposant une certaine dépendance entre la fréquence et la sévérité des sinistres. Nous considérons des modèles collectifs de risque avec différentes structures de dépendance telles que des modèles impliquant des lois mélanges d’Erlang multivariées ou, dans un cadre plus général, des modèles basés sur des copules bivariées ou multivariées. Nous utilisons également les copules Archimédiennes et Archimédiennes hiérarchiques afin de modéliser la dépendance entre les composantes de la somme aléatoire représentant le montant de sinistre global. En nous basant encore une fois sur la représentation de notre modèle sous forme d’un mélange commun, nous adaptons la méthodologie computationnelle présentée au chapitre 2 pour calculer la fonction de masse de probabilité d’une somme aléatoire incorporant une dépendance hiérarchique. Finalement, dans le cinquième chapitre, nous soulignons l’utilité des modèles avec mélange commun et nous étudions plus en détail les lois exponentielles mélange dans leurs versions univariée et multivariée et nous expliquons leur lien étroit avec les copules Archimédiennes et Archimédiennes hiérarchiques. Nous proposons également plusieurs nouvelles distributions et nous établissons leurs liens avec des distributions connues.
Risk dependence modelling has become an increasingly important task for the solvency of financial institutions and insurance companies. The independence assumption between risks is sometimes realistic and facilitates risk assessment, aggregation and allocation. However, in most cases individual risks are influenced by at least one common factor, such as the economic environment, geographical regions or climatic conditions, and it is therefore less realistic or even dangerous to assume independence between risks. In the literature, such a case can be modelled by common mixture models. These models have many applications in insurance and finance. The aim of this thesis is to explore the dependence models constructed using common mixtures and to bring out, with the use of several applications, the riskiness of considering the independence between risks within an insurance company or a financial institution. In particular, the focus is on the exponential mixture. Exponential mixture distributions are on the basis of this thesis. The first chapter is a general introduction to models with common mixtures and introduces the concepts that will be used in the other chapters. In the second chapter, we consider a portfolio of risks represented by a vector of random variables whose joint distribution function is defined by an Archimedean copula or a nested Archimedean copula. We examine the computation of the distribution of the sum function or a variety of functions of these random variables. Based on the computational methodology presented in this chapter, we examine risk models regarding aggregation, capital allocation and ruin problems. Moreover, by using such a dependency structure with specific marginals, we obtain explicit expressions for several aggregated risk quantities such as its probability mass function, its distribution function, and its TVaR. The exchangeability of the Archimedean copulas implies that all margins are equal. To generalize Archimedean copulas to allow asymmetries, several researchers use a hierarchical structure obtained by nesting several Archimedean copulas. However, it is difficult to validate the nesting condition when the copulas involved belong to different Archimedean families. To solve this problem, we present, in the third chapter, a new imbrication method via the construction of the multivariate compound distributions. By introducing several parameters, a large spectrum of dependency structures can be achieved by this new construction, which seems very interesting for practical applications. Efficient sampling and aggregation algorithms are also presented. Based on both Chapters 2 and 3, we propose and examine in detail, in the fourth chapter, a new extension to the collective risk model assuming a certain dependence between the frequency and the severity of the claims. We consider collective risk models with different dependence structures such as models based on multivariate mixed Erlang distributions, models involving bivariate or multivariate copulas, or in a more general setting, Archimedean and hierarchical Archimedean copulas. Once again, based on the common mixture representation, we adapt the computational methodology presented in Chapter 2 to compute the probability mass function of a random sum incorporating a hierarchical Archimedean dependency. Finally, in the last chapter, we study, in more details, the exponential mixture distributions in their univariate and multivariate versions and we explain their close relationship to Archimedean and hierarchical Archimedean copulas. We also derive several new distributions, and we establish their links with pre-existent distributions. Keywords : Common mixture models, Exponential mixture, Bernoulli mixture, Archimedean copulas, Nested Archimedean copulas, Compounding, Marshall-Olkin, Hierarchical dependence structures.
Albardan, Mahmoud. "Combinaison robuste à la dépendance entre classifieurs dans un contexte d’apprentissage décentralisé". Thesis, Lille 1, 2018. http://www.theses.fr/2018LIL1I050/document.
Texto completo da fonteMachine learning is a rapidly growing field of science concerning both the number of methods used and the amount of data available for users. Classification is thus affected by these changes. The presence of a large number of classification algorithms thus encourages the creation of global systems that are based on classifier ensembles, in the purpose of providing efficient solutions to complex classification problems. This is the main motivation behind our thesis whose subject is the study of multi-classifiers systems. A multi-classifiers system is a set of classifiers whose decisions is aggregated according to a specific architecture and using a combination rule. There are different types architectures such as parallel, sequential or hybrid architectures. In this thesis, we are only interested in classifier ensembles having a parallel architecture. Briefly, the purpose of my research is then the design of multi-classifiers systems to improve classification performance and to offer certain level of robustness. However, the design of such systems, that can be seen as a fusion of different sources of information and which will be trained on correlated learning examples, generates dependence in the individual decisions of classifiers and consequently impose the creation of classifier ensembles that are adapted to dependency between individual classifiers. Thus, we propose two approaches that are the main contributions of this thesis. The first one is a possibilistic approach based on a well-known combination rule in fuzzy logic, the t-norm, while the second is a probabilistic approach based on a copula function which are models of dependence between random variables
Houdard, Clément. "Analyse de solutions pour limiter l'érosion externe du talus arrière d'une digue en terre soumise à la houle : une approche basée sur la théorie des copules et l’analyse de sensibilité globale". Electronic Thesis or Diss., Université Gustave Eiffel, 2023. http://www.theses.fr/2023UEFL2070.
Texto completo da fonteThis study presents a comprehensive analysis framework for an earthen dyke located in Camargue, France, which is regularly subjected to erosion on the landward slope. The aim of the study is to improve the resilience of the dyke by providing a reliable model of damage frequency. To achieve this, we developed a system that combines copula theory, empirical wave propagation, and overtopping equations, as well as a global sensitivity analysis. The system provides the return period of erosion damage on a set dyke and recommendations for dyke reinforcement and model self-improvement. The global sensitivity analysis requires calculating a high number of return periods over random observations of the tested parameters. This provides a distribution of the return periods and a more general approach to the behavior of the dyke. The results show a return period peak around the two-year mark, which is close to reported observations. However, the distribution is skewed, and the mean value is less reliable as a measure of dyke safety. The global sensitivity analysis results show that no particular category of dyke features contributes significantly more to the uncertainty of the system. The highest contributing factors are the dyke height, the critical velocity, and the coefficient of seaward slope roughness. These results underline the importance of good dyke characterization to improve the predictability of return period estimations. The obtained return periods have been confirmed by current in-situ observations, but the uncertainty increases for the most severe events due to the lack of long-term data. Some improvements to the system have been explored for future use
Depire, Alexandre. "Modélisation Markovienne – Modèles de régression de copules et valeurs extrêmes – Application aux systèmes d’aide à la conduite". Reims, 2008. http://theses.univ-reims.fr/exl-doc/GED00000749.pdf.
Texto completo da fonteThe thesis gets organized in two major parties. The first part turns on the intelligent transportation system (autonomous cruise control). In the first chapter we study strategies of drivers and confirm a hypothesis of F. Saad. The second chapter tackles the cellular automaton. The third chapter suggests validation of an assumption in the field of the driver psychology by the use of the markovian models. The last chapter deals with the input-output hidden markov models. A theoretical framework is presented. The main purpose is the study of tools for the evaluation of such systems through data with / without the system and real data, not controlled. The important notion is the concept of scene, as defined the changes in the dependence between several indicators. The central object in the dependence is the copula, the heart of the second part. The first chapter is a state of the art, refer to the measures of dependence and function of linkage. The second chapter tackles a measure of a multivariate dependence. We demonstrate a formula about the mutual information. In the third chapter, an extension of the cox model in bivariate case is presented, based on extreme value copulas. Some approximation results and the convergence are proved. We give an application on real data from lavia system (speed limiter). The fourth chapter is about the estimating of the dependence function in the bivariate case. We prove the uniform convergence and give the asymptotic law of our estimator
Fontaine, Charles. "Utilisation de copules paramétriques en présence de données observationnelles : cadre théorique et modélisations". Thesis, Montpellier, 2016. http://www.theses.fr/2016MONTT009/document.
Texto completo da fonteObservational studies (non-randomized) consist primarily of data with features that are in fact constraining within a classical statistical framework. Indeed, in this type of study, data are rarely continuous, complete, and independent of the therapeutic arm the observations are belonging to. This thesis deals with the use of a parametric statistical tool based on the dependence between the data, using several scenarios related to observational studies. Indeed, thanks to the theorem of Sklar (1959), parametric copulas have become a topic of interest in biostatistics. To begin with, we present the basic concepts of copulas, as well as the main measures of association based on the concordance founded on an analysis of the literature. Then, we give three examples of application of models of parametric copulas for as many cases of specific data found in observational studies. We first propose a strategy of modeling cost-effectiveness analysis based essentially on rewriting the joint distribution functions, while discarding the use of linear regression models. We then study the constraints relative to discrete data, particularly in a context of non-unicity of the copula function. We rewrite the propensity score, thanks to an innovative approach based on the extension of a sub-copula. Finally, we introduce a particular type of missing data: right censored data, in a regression context, through the use of semi-parametric copulas
L'Moudden, Aziz. "Une généralisation de la copule de Khoudraji : copules engendrées par des fonctions complètement monotones". Master's thesis, Université Laval, 2011. http://hdl.handle.net/20.500.11794/22659.
Texto completo da fonteSloma, Przemyslaw. "Contribution to the weak convergence of empirical copula process : contribution to the stochastic claims reserving in general insurance". Thesis, Paris 6, 2014. http://www.theses.fr/2014PA066563/document.
Texto completo da fonteThe aim of this thesis is twofold. First, we concentrate on the study of weak convergence of weighted empirical copula processes. We provide sufficient conditions for this convergence to hold to a limiting Gaussian process. Our results are obtained in the framework of convergence in the Banach space $L^{p}$ ($1\leq p <\infty $). Statistical applications to goodness of fit (GOF) tests for copulas are given to illustrate these results. We pay special attention to GOF tests based on Cramér-von Mises type statistics. Second, we discuss the problem of stochastic claims reserving in general non-life insurance. Stochastic models are needed in order to assess the variability of the claims reserve. The starting point of this thesis is an observed inconsistency between the approaches used in practice and that suggested in the literature. To fill this gap, we present a general tool for measuring the uncertainty of reserves in the framework of ultimate (Chapter 3) and one-year time horizon (Chapter 4), based on the Chain-Ladder method
Benoumechiara, Nazih. "Traitement de la dépendance en analyse de sensibilité pour la fiabilité industrielle". Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS047.
Texto completo da fonteStructural reliability studies use probabilistic approaches to quantify the risk of an accidental event occurring. The dependence between the random input variables of a model can have a significant impact on the results of the reliability study. This thesis contributes to the treatment of dependency in structural reliability studies. The two main topics covered in this document are the sensitivity analysis for dependent variables when the dependence is known and, as well as the assessment of a reliability risk when the dependence is unknown. First, we propose an extension of the permutation-based importance measures of the random forest algorithm towards the case of dependent data. We also adapt the Shapley index estimation algorithm, used in game theory, to take into account the index estimation error. Secondly, in the case of dependence structure being unknown, we propose a conservative estimate of the reliability risk based on dependency modelling to determine the most penalizing dependence structure. The proposed methodology is applied to an example of structural reliability to obtain a conservative estimate of the risk
Derennes, Pierre. "Mesures de sensibilité de Borgonovo : estimation des indices d'ordre un et supérieur, et application à l'analyse de fiabilité". Thesis, Toulouse 3, 2019. http://www.theses.fr/2019TOU30039.
Texto completo da fonteIn many disciplines, a complex system is modeled by a black box function whose purpose is to mimic the real system behavior. Then, the system is represented by an input-output model, i.e, a relationship between the output Y (the observation made on the system) and a set of external parameters Xi (typically representing physical variables). These parameters are usually assumed to be random in order to take phenomenological uncertainties into account. Then, global sensitivity analysis (GSA) plays a crucial role in the handling of these uncertainties and in the understanding of the system behavior. This study is based on the estimation of importance measures which aim at identifying and ranking the different inputs with respect to their influence on the model output. Variance-based sensitivity indices are one of the most widely used GSA measures. They are based on Sobol's indices which express the share of variance of the output that is due to a given input or input combination. However, by definition they only study the impact on the second-order moment of the output which may a restrictive representation of the whole output distribution. The central subject of this thesis is an alternative method, introduced by Emanuele Borgonovo, which is based on the analysis of the whole output distribution. Borgonovo's importance measures present very convenient properties that justify their recent gain of interest, but their estimation is a challenging task. Indeed, the initial definition of the Borgonovo's indices involves the unconditional and conditional densities of the model output, which are unfortunately unknown in practice. Thus, the first proposed methods led to a high computational burden especially since the black box function may be very costly-to-evaluate. The first contribution of this thesis consists in proposing new methodologies for estimating first order Borgonovo importance measures which quantify the influence of the output Y relatively to a scalar input Xi. First, we choose to adopt the reinterpretation of the Borgonovo indices in term of measure of dependence, i.e, as a distance between the joint density of Xi and Y and the product distribution. In addition, we develop an estimation procedure combining an importance sampling procedure and Gaussian kernel approximation of the output density and the joint density. This approach allows the computation of all first order Borgonovo with a low budget simulation, independent to the model dimension. However, the use of Gaussian kernel estimation may provide inaccurate estimates for heavy tail distributions. To overcome this problem, we consider an alternative definition of the Borgonovo indices based on the copula formalism
Aleiyouka, Mohalilou. "Sur la dépendance des queues de distributions". Thesis, Normandie, 2018. http://www.theses.fr/2018NORMLH28/document.
Texto completo da fonteThe modeling of the dependence between several variables can focus either on the positive or negative correlation between the variables, or on other more effective ways, which determine the tails dependence of distributions.In this thesis, we are interested in the tail dependence of distributions, by presenting some properties and results. Firstly, we obtain the limit tail dependence coefficient for the generalized hyperbolic law according to different parameter values of this law. Then, we exhibit some properties and results of die extremal dependence coefficient in the case where the random variables follow a unitary Fréchet law.Finally, we present a Real Time Database ManagementSystems (RDBMS). The goal is to propose probabilistic models to study thebehavior of real-time transactions, in order to optimize its performance
Sarazin, Marianne. "Elaboration d'un score de vieillissement : propositions théoriques". Phd thesis, Université Jean Monnet - Saint-Etienne, 2013. http://tel.archives-ouvertes.fr/tel-00994941.
Texto completo da fonteRomdhani, Héla. "Mesures d'association pour des modèles de copules multidimensionnelles". Doctoral thesis, Université Laval, 2013. http://hdl.handle.net/20.500.11794/24916.
Texto completo da fonteIn this thesis we are interested in measuring the dependence under copula models. We deal with three problems: the measure of association in the bivariate case in the presence of lower detection limits, the measure of association for clustered data and the measure of association for two-level hierarchical data. The first problem, independent of the other two, deals with the measure of association between two variables subject to fixed left censoring due to the presence of lower detection limits. We define a conditional version of Kendall’s tau to measure the association between such variables. We provide a nonparametric estimator of this measure and study its asymptotic properties. We then assume an Archimedean copula model and deduce an estimator for the copula’s Kendall’s tau. A goodness-of-fit test for the assumed copula is developed. The second problem deals with the measure of intra-class association for clustered data such that observations within each group are exchangeable. For this, we introduce an exchangeable version of Kendall’s tau as a measure of intra-class dependance and provide a nonparametric estimator for this measure. Its asymptotic properties are investigated under a multivariate exchangeable copula model. We derive an estimator of the intra-class correlation coefficient for data drawn from an elliptical distribution. The asymptotic properties of this estimator are investigated under a generalized oneway ANOVA model. Finally, we develop an intra-class independence test based on Kendall’s tau. The third problem is an extension of the second to the case of hierarchical data with a set of subgroups nested into groups, such that the units within each subgroup are exchangeable and the subgroups belonging to the same group are themselves exchangeable. We define two association measures based on the exchangeable Kendall’s tau and propose nonparametric estimators for these measures. We investigate their asymptotic properties under hierarchical copula models satisfying some properties of partial exchangeability. For data drawn from meta-elliptical hierarchical copulas we deduce estimators for the intra-class correlation coefficients associated to groups and subgroups respectively. We also develop procedures for testing the effects of groups and subgroups.
Tounkara, Fode. "Modèles de copules Archimédiennes pour données de Bernoulli corrélées". Doctoral thesis, Université Laval, 2015. http://hdl.handle.net/20.500.11794/26528.
Texto completo da fonteThis thesis introduces and explores a new class of probability models for exchangeable clustered binary data. In these models, the conditional probability of success is characterized by a function of the marginal probability of success and a positive cluster-specific random effect. The marginal probabilities are modeled using the logit and complementary log-log link functions. The distribution of the random effect contains an association parameter that is estimated to give a measure of the strength of the within-cluster residual dependence that is not accounted for by the margins. We show that the random effect distributions can be related to exchangeable Archimedean copula models, thus giving new insights on such models. The copula approach offers many advantages. Indeed, the family of Archimedean copulas provides a large class of models for over-dispersion in a Bernoulli experiment. From a statistical perspective, the marginal likelihood function for the sample data has an explicit expression, the maximum likelihood methods are then easy to implement and computationally straightforward. Based on the proposed models, four applications are considered. First, we investigate the construction of profile likelihood confidence interval (PLCI) for the intra-cluster correlation coefficient (ICC). The second application is concerned with an heterogeneity in capture probabilities in a mark-recapture study for estimating the size of a closed population. The third contribution deals with the estimation in small areas, the fourth and final, independent of the other three, analyzes the socioeconomic characteristics of men who prefer to marry girls under 18 years old. In the first application, we consider a simple case, without covariates and construct maximum likelihood inference procedures for the intra-cluster correlation using several specifications of Archimedean copulas. The selection of a particular model is carried out using the Akaike information criterion (AIC). Profile likelihood confidence intervals for the ICC are constructed and their performance are assessed in a simulation experiment. The sensitivity of the inference to the specification of the copula family is also investigated through simulations. Numerical examples are presented. We compare our approach with that proposed under the Beta-binomial model and with the modified Wald interval method proposed by Zou and Donner (2004). One of the important findings of these studies is that the profile confidence interval obtained under our models presents nice properties, even when the number of clusters is small. Model selection is an important step: if the model is poorly specified, then this could lead to erroneous results. The second application, an extension of the first one to accommodate cluster level covariates, is concerned with an heterogeneity in capture probabilities in a capture-recapture study for estimating the size of a closed population. Unit level covariates are recorded on the units that are captured and copulas are used to model the residual heterogeneity that is not accounted for by covariates. Several models for the unobserved heterogeneity are available and the marginal capture probability is expressed using the Logit and the complementary Log-Log link functions. The parameters are estimated using a conditional likelihood constructed with the data obtained on the units caught at least once. The population size is estimated using a Horvitz-Thompson estimator constructed using the estimated probabilities that a unit is caught at least once. This generalizes the model of Huggins (1991) that does not account for a residual heterogeneity. The sensitivity of the inference to the specification of a model is also investigated through simulations. A numerical example is presented. The third application uses the models of the first two in order to estimate small area proportions. We apply Bayes techniques using a new class of probability models, to estimate small area proportions. The Bayesian inference under the proposed models consists in obtaining the posterior distribution of the random effect and its Laplace transform. This posterior Laplace transform is then used to find Bayes estimates of small area proportions. We develop a comparison between the Best Predictor (BP) and the Best Linear Unbiased Predictor (BLUP). The model parameters are estimated using the maximum likelihood (ML) method. Under the proposed model, the likelihood function and the best predictor (BP) of small area proportion have closed form expressions. Model parameters are replaced by their ML estimates in the BP to obtain the empirical best predictor (EBP). We use the Akaike information criterion (AIC) for selecting a particular model. We propose the jackknife method to estimate the mean square error of the empirical Bayes predictor. Empirical results obtained from simulated and real data are also presented. The fourth and last problem addressed in this thesis, independently of the others three, investigates socioeconomic characteristics of men who prefer to marry girls under 18 years. We consider the data from the 2006 DHS Niger and use a bivariate Archimedean copula to model the association between education level (discrete) of men and their pre-marital income (continuous). We present the likelihood function for a sample from this pair of mixed random variables, and derive an estimate of the dependence parameter using a semiparametric procedure where margins are estimated by their empirical equivalents. We use the jackknife method to estimate the standard error. We use a Wald-type procedure, to perform a parametric hypothesis test of equality between the association of the socio economic characteristics of men who marry underage girls and that of men who marry older women instead. These test results contribute to the validity of our theory that men who marry girls under 18 years old have a low level of education and income pre-marital, when compared to men who did not.
Bargès, Mathieu. "Modèles de dépendance dans la théorie du risque". Phd thesis, Université Claude Bernard - Lyon I, 2010. http://tel.archives-ouvertes.fr/tel-00736207.
Texto completo da fonteKhadraoui, Lobna. "Sélection de copules archimédiennes dans un modèle semi-paramétrique". Master's thesis, Université Laval, 2018. http://hdl.handle.net/20.500.11794/30251.
Texto completo da fonteThis work considers a semi-parametric linear model with error terms modeled by a copula chosen from the Archimedean family or the normal copula. The modeling of errors by a copula provides flexibility and makes it possible to characterize the dependency structure in a simple and effective manner. The simplicity lies in the fact that a single parameter α controls the degree of dependency present in the data. The efficiency is in the fact that this semi-parametric model weakens standard assumptions often encountered in applied statistics namely normality and independence. After an implementation of the model based on a copula we proposed a theoretical study on the asymptotic behavior of the estimator of the dependence parameter α by showing its consistency and its asymptotic normality under classical assumptions of regularity. Estimation of the model parameters is performed by maximizing a pseudo-likelihood. The selection of the best copula that fits the data for each case is based on the Akaike selection criterion. A comparison with the criterion of cross-validation is presented as well. Finally, a numerical study on simulated and real data sets is proposed.
Monwanou, Mondji Herbert. "Estimation du paramètre d'une copule archimedienne en présence de censure dépendante". Master's thesis, Université Laval, 2016. http://hdl.handle.net/20.500.11794/26856.
Texto completo da fonteConventional methods of survival analysis including non-parametric Kaplan-Meier (1958) assume independence between time to death and time to censoring. But this independence assumption is not always sustainable. Thus, several authors have developed methods to take into account the dependence by making assumptions about the relationship between the two times. In this paper, we proposed a method to estimate the dependence in case of competing risk data using the copula-graphic estimator for Archimedean copula (Rivest and Wells, 2001) and assuming knowledge of the distribution of censoring time. Then we studied the consistency of this estimator through simulations and applied to a real dataset.
Binois, Mickaël. "Uncertainty quantification on pareto fronts and high-dimensional strategies in bayesian optimization, with applications in multi-objective automotive design". Thesis, Saint-Etienne, EMSE, 2015. http://www.theses.fr/2015EMSE0805/document.
Texto completo da fonteThis dissertation deals with optimizing expensive or time-consuming black-box functionsto obtain the set of all optimal compromise solutions, i.e. the Pareto front. In automotivedesign, the evaluation budget is severely limited by numerical simulation times of the considered physical phenomena. In this context, it is common to resort to “metamodels” (models of models) of the numerical simulators, especially using Gaussian processes. They enable adding sequentially new observations while balancing local search and exploration. Complementing existing multi-objective Expected Improvement criteria, we propose to estimate the position of the whole Pareto front along with a quantification of the associated uncertainty, from conditional simulations of Gaussian processes. A second contribution addresses this problem from a different angle, using copulas to model the multi-variate cumulative distribution function. To cope with a possibly high number of variables, we adopt the REMBO algorithm. From a randomly selected direction, defined by a matrix, it allows a fast optimization when only a few number of variables are actually influential, but unknown. Several improvements are proposed, such as a dedicated covariance kernel, a selection procedure for the low dimensional domain and of the random directions, as well as an extension to the multi-objective setup. Finally, an industrial application in car crash-worthiness demonstrates significant benefits in terms of performance and number of simulations required. It has also been used to test the R package GPareto developed during this thesis
Abdallah, Anas. "Modèles de dépendance hiérarchique pour l'évaluation des passifs et la tarification en actuariat". Doctoral thesis, Université Laval, 2016. http://hdl.handle.net/20.500.11794/27001.
Texto completo da fonteThe objective of this thesis is to propose innovative hierarchical approaches to model dependence within and between risks in non-life insurance in general, and in a loss reserving context in particular. One of the most critical problems in property/casualty insurance is to determine an appropriate reserve for incurred but unpaid losses. These provisions generally comprise most of the liabilities of a non-life insurance company. The global provisions are often determined under an assumption of independence between the lines of business. However, most risks are related to each other in practice, and this correlation needs to be taken into account. Recently, Shi and Frees (2011) proposed to include dependence between lines of business in a pairwise manner, through a copula that captures dependence between two equivalent cells of two different runoff triangles. In this thesis, we propose to generalize this model with two different approaches. Firstly, by using hierarchical Archimedean copulas to accommodate correlation within and between lines of business, and secondly by capturing this dependence through random effects. The first approach will be presented in chapters 2 and 3. In chapter 2, we use partially nested Archimedean copulas to capture dependence within and between two lines of business, through calendar year effects. In chapter 3, we use fully nested Archimedean copulas, to accommodate dependence between more than two lines of business. A copula-based risk aggregation model is also proposed to accommodate dependence. The inference for the dependence structure is performed with a rank-based methodology to bring more robustness to the estimation. In chapter 4, we introduce the Sarmanov family of bivariate distributions to a loss reserving context, and show that its flexibility proves to be very useful for modeling dependence between loss triangles. This dependence is captured by random effects, through calendar years, accident years or development periods. Closed-form expressions are given, and a real life illustration is shown again. In chapter 5, we use the Sarmanov family of bivariate distributions in a dynamic framework, where the random effects are considered evolutionary and evolve over time, to update the information and allow more weight to more recent claims. Hence, we propose an innovative way to jointly model the dependence between risks and over time with an illustration in a ratemaking context. Finally, a brief conclusion recalls the main contributions of this thesis and provides insights into future research and possible extensions to the proposed works.
Derien, Anthony. "Solvabilité 2 : une réelle avancée ?" Phd thesis, Université Claude Bernard - Lyon I, 2010. http://tel.archives-ouvertes.fr/tel-00733700.
Texto completo da fontePougaza, Doriano-Boris. "Utilisation de la notion de copule en tomographie". Phd thesis, Université Paris Sud - Paris XI, 2011. http://tel.archives-ouvertes.fr/tel-00684637.
Texto completo da fonteGribkova, Svetlana. "Contributions à l'inférence statistique en présence de censure multivariée". Thesis, Paris 6, 2014. http://www.theses.fr/2014PA066178/document.
Texto completo da fonteThe main purpose of this thesis is to explore several approaches for studying multivariate censored data: nonparametric estimation of the joint distribution function, modeling dependence with copulas and k-clustering for the exploratory analysis. Chapter 1 presents the general framework and the contributions of this thesis. Chapter 2 deals with the estimation of the joint distribution function of two censored variables in a simplified survival model in which the difference between two censoring variables is observed. We provide a new nonparametric estimator of the joint distribution function and we establish the asymptotic normality of the integrals with respect to its associated measure. Chapter 3 is devoted to nonparametric copula estimation under bivariate censoring. We provide a discrete and two smooth copula estimators along with two estimators of its density. The discrete estimator can be seen as an extension of the empirical copula under censoring. Chapter 4 provides a new exploratory approach for censored data analysis. We consider a multivariate configuration with one variable subjected to censoring and the others completely observed. We extend the probabilistic k-quantization method in the case of random vector with one censored component. The definitions of the empirical distortion and of empirically optimal quantizer are generalized in presence of one-dimensional censoring. We study the asymptotic properties of the distortion of the empirically optimal quantizer and we provide a non-asymptotic exponential bound for the rate of convergence. Our results are then applied to construct a new two-step clustering algorithm for censored data
Ben, Hadj Fredj Mejdi. "Les déterminants macro-économiques et financiers de l'efficience bancaire de pays émergents : cas de la Tunisie". Thesis, Tours, 2016. http://www.theses.fr/2016TOUR1005.
Texto completo da fonteOur objective of this work is to study the efficiency of the Tunisian financial market before and after the Jasmin revolution of 2011 and identify macro-economic and financial factors that influence the efficiency score of this market. Our methodology is to use at first multivariate GARCH model to estimate the correlation between market returns and those of individual banks and the Beta coefficient. As this model assumes the residues that follow the multivariate normal law is untested in practice, we used in a second step the copula theory to provide more flexibility in modeling multivariate data. The most influential factors are determined using the linear regression model, the panel data model and TOBIT model. The empirical results show that the Tunisian market is not efficient either before or after the revolution. Many actions are proposed to improve the degree of efficiency of this market
Le, Faou Yohann. "Contributions à la modélisation des données de durée en présence de censure : application à l'étude des résiliations de contrats d'assurance santé". Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS527.
Texto completo da fonteIn this thesis, we study duration models in the context of the analysis of contract termination time in health insurance. Identified from the 17th century and the original work of Graunt J. (1662) on mortality, the bias induced by the censoring of duration data observed in this context must be corrected by the statistical models used. Through the problem of the measure of dependence between successives durations, and the problem of the prediction of contract termination time in insurance, we study the theoretical and practical properties of different estimators that rely on a proper weighting of the observations (the so called IPCW method) designed to compensate this bias. The application of these methods to customer value estimation is also carefully discussed
Faugeras, Olivier Paul. "Contributions à la prévision statistique". Paris 6, 2008. http://www.theses.fr/2008PA066436.
Texto completo da fonteBen, Abdallah Nadia. "Modeling sea-level rise uncertainties for coastal defence adaptation using belief functions". Thesis, Compiègne, 2014. http://www.theses.fr/2014COMP1616.
Texto completo da fonteCoastal adaptation is an imperative to deal with the elevation of the global sealevel caused by the ongoing global warming. However, when defining adaptationactions, coastal engineers encounter substantial uncertainties in the assessment of future hazards and risks. These uncertainties may stem from a limited knowledge (e.g., about the magnitude of the future sea-level rise) or from the natural variabilityof some quantities (e.g., extreme sea conditions). A proper consideration of these uncertainties is of principal concern for efficient design and adaptation.The objective of this work is to propose a methodology for uncertainty analysis based on the theory of belief functions – an uncertainty formalism that offers greater features to handle both aleatory and epistemic uncertainties than probabilities.In particular, it allows to represent more faithfully experts’ incomplete knowledge (quantiles, intervals, etc.) and to combine multi-sources evidence taking into account their dependences and reliabilities. Statistical evidence can be modeledby like lihood-based belief functions, which are simply the translation of some inference principles in evidential terms. By exploiting the mathematical equivalence between belief functions and random intervals, uncertainty can be propagated through models by Monte Carlo simulations. We use this method to quantify uncertainty in future projections of the elevation of the global sea level by 2100 and evaluate its impact on some coastal risk indicators used in coastal design. Sea-level rise projections are derived from physical modelling, expert elicitation, and historical sea-level measurements. Then, within a methodologically-oriented case study,we assess the impact of climate change on extreme sea conditions and evaluate there inforcement of a typical coastal defence asset so that its functional performance is maintained
Deschatre, Thomas. "Dependence modeling between continuous time stochastic processes : an application to electricity markets modeling and risk management". Thesis, Paris Sciences et Lettres (ComUE), 2017. http://www.theses.fr/2017PSLED034/document.
Texto completo da fonteIn this thesis, we study some dependence modeling problems between continuous time stochastic processes. These results are applied to the modeling and risk management of electricity markets. In a first part, we propose new copulae to model the dependence between two Brownian motions and to control the distribution of their difference. We show that the class of admissible copulae for the Brownian motions contains asymmetric copulae. These copulae allow for the survival function of the difference between two Brownian motions to have higher value in the right tail than in the Gaussian copula case. Results are applied to the joint modeling of electricity and other energy commodity prices. In a second part, we consider a stochastic process which is a sum of a continuous semimartingale and a mean reverting compound Poisson process and which is discretely observed. An estimation procedure is proposed for the mean reversion parameter of the Poisson process in a high frequency framework with finite time horizon, assuming this parameter is large. Results are applied to the modeling of the spikes in electricity prices time series. In a third part, we consider a doubly stochastic Poisson process with stochastic intensity function of a continuous semimartingale. A local polynomial estimator is considered in order to infer the intensity function and a method is given to select the optimal bandwidth. An oracle inequality is derived. Furthermore, a test is proposed in order to determine if the intensity function belongs to some parametrical family. Using these results, we model the dependence between the intensity of electricity spikes and exogenous factors such as the wind production
Zheng, Ce. "Impulsive and dependent interference in IoT networks". Thesis, Lille 1, 2020. http://www.theses.fr/2020LIL1I064.
Texto completo da fonteThe number of devices in wireless Internet of Things (IoT) networks is now rapidly increasing and is expected to continue growing in the coming years. To support this massive connectivity, a number of new technologies, collectively known as Low Power Wide Area Network (LPWAN), have been developed. Many devices in LPWANs limit their transmissions by duty cycle constraints; i.e., the proportion of time allocated for transmission. For nearby wireless networks using the same time-frequency resources, the increasing number of devices leads to a high level of unintended signals, known as interference. In this thesis, we characterize the statistics of interference arising from LPWANs, with a focus on protocols related to Narrowband IoT (NB-IoT) and emerging approaches such as Sparse Code Multiple Access (SCMA). Such a characterization is critical to improve signal processing at the receiver in order to mitigate the interference. We approach the characterization of the interference statistics by exploiting a mathematical model of device locations, signal attenuation, and the access protocols of individual interfering devices. While there has been recent work developing empirical models for the interference statistics, this has been limited to studies of the interference power, which has limited utility in receiver design. The approach adopted in this thesis has the dual benefits of providing a model for the amplitude and phase statistics and while also yielding insights into the impact of key network parameters. The first contribution in this work is to revisit interference in a single subcarrier system, which is widely used in current implementations of IoT networks. A basic model in this scenario distributes interfering devices according to a homogeneous Poisson point process. It has been long known that the resulting interference is well approximated via an α-stable model, rather than a Gaussian model. In this work, the α-stable model is shown via theoretical and simulation results to be valid in a wider range of models, including the presence of guard zones, finite network radii, and non-Poisson point processes governing device locations. The second contribution in this thesis is the study, for the first time, of interference statistics in multi-carrier IoT networks, including those that exploit NB-IoT and SCMA. Motivated by the results in the single subcarrier setting, a multivariate model based on α-stable marginals and copula theory is developed. This model is verified by extensive simulations and further justified via a new, near-optimal, parameter estimation algorithm, which has very low complexity.The third part of this thesis applies the characterizations of the interference statistics to receiver design. A new design for nonlinear receivers is proposed that can significantly outperform the state-of-the-art in multicarrier IoT systems. When receivers are restricted to be linear, the optimal structure is identified and the bit error rate characterized. Numerical results also illustrate how the average quantity of data interfering devices are required to transmit affects the receiver performance
Iacopini, Matteo. "Essays on econometric modelling of temporal networks". Thesis, Paris 1, 2018. http://www.theses.fr/2018PA01E058/document.
Texto completo da fonteGraph theory has long been studied in mathematics and probability as a tool for describing dependence between nodes. However, only recently it has been implemented on data, giving birth to the statistical analysis of real networks.The topology of economic and financial networks is remarkably complex: it is generally unobserved, thus requiring adequate inferential procedures for it estimation, moreover not only the nodes, but the structure of dependence itself evolves over time. Statistical and econometric tools for modelling the dynamics of change of the network structure are lacking, despite their increasing requirement in several fields of research. At the same time, with the beginning of the era of “Big data” the size of available datasets is becoming increasingly high and their internal structure is growing in complexity, hampering traditional inferential processes in multiple cases.This thesis aims at contributing to this newborn field of literature which joins probability, economics, physics and sociology by proposing novel statistical and econometric methodologies for the study of the temporal evolution of network structures of medium-high dimension
Dubecq, Simon. "Stress-Test Exercises and the Pricing of Very Long-Term Bonds". Phd thesis, Université Paris Dauphine - Paris IX, 2013. http://tel.archives-ouvertes.fr/tel-00871760.
Texto completo da fonteAjavon, Ayi. "Sur les prolongements de sous-copules". Thèse, 2015. http://hdl.handle.net/1866/11969.
Texto completo da fonteThe extension of subcopulas is an important domain. One of possible applications is the nonparametric estimation of a copula: it consists of the smoothing of a subcopula (the empirical copula) while preserving the copulas properties. In Chapter 2, we present an extension of the empirical copula based on the tensor product of splines functions. Our estimators are bona fide estimators of the copula. Chapter 3 tackles the problem of finding all possible extensions of a given subcopula. This subject has been treated in the literature but these characterizations do not apply on very general spaces. Chapter 4 deals with the following problem: finding the expression of the upper bound of the extensions of a finite subcopula in dimension 3.
Pham, David. "Densités de copules archimédiennes hiérarchiques". Thèse, 2012. http://hdl.handle.net/1866/8529.
Texto completo da fonteNested Archimedean copulas recently gained interest since they generalize the well-known class of Archimedean copulas to allow for partial asymmetry. Sampling algorithms and strategies have been well investigated for nested Archimedean copulas. However, for likelihood based inference such as estimation or goodness-of-fit testing it is important to have the density. The present work fills this gap. After a short introduction on copula and nested Archimedean copulas, a general formula for the derivatives of the nodes and inner generators appearing in nested Archimedean copulas is developed. This leads to a tractable formula for the density of nested Archimedean copulas. Various examples including famous Archimedean families and transformations of such are given. Furthermore, a numerically efficient way to evaluate the log-density is presented.
Ndoye, Babacar. "Étude de la puissance de tests de symétrie radiale pour copules multidimensionnelles sous de la dépendance de type Fisher". Thèse, 2020. http://depot-e.uqtr.ca/id/eprint/9423/1/eprint9423.pdf.
Texto completo da fonteSimard, Clarence. "Modélisation du carnet d'ordres limites et prévision de séries temporelles". Thèse, 2014. http://hdl.handle.net/1866/11670.
Texto completo da fonteThis thesis is structured as follows. After a first chapter of introduction, Chapter 2 exposes as simply as possible different notions that are going to be used in the two first papers. First, we discuss the main steps required to build stochastic integrals for semimartingales with space parameters. Secondly, we describe the main results of risk neutral evaluation theory and, finally, we give a short description of an optimization method known as duality. Chapters 3 and 4 consider the problem of modelling illiquidity, which is covered by two papers. The first one proposes a continuous time model for the structure and the dynamic of the limit order book. The dynamic of a portfolio for an investor using market orders is deduced and conditions to rule out arbitrage are given. With the help of Itô’s generalized formula, it is also possible to write the value of the portfolio as a stochastic differential equation. A complete example of market model along with a calibration method is also given. In the second paper, written in collaboration with Bruno Rémillard, we propose a similar model with discrete time trading. We study the problem of derivatives pricing and give explicit formulas for European option prices. Specific conditions to rule out arbitrage are also provided. Using the dual optimization method, we show that the price of European options can be written as the optimization of an expectation over a set of probability measures. Chapter 5 contained the third paper and studies a different topic. In this paper, also written with Bruno Rémillard, we propose a forecasting method for time series based on multivariate copulas. To provide a better understanding of the proposed method, with the help of numerical experiments, we study the effect of the strength and the structure of the different dependencies on predictions performance. Since copulas allow to isolate the dependence structure and marginal distributions, we study the impact of different marginal distributions on predictions performance. Finally, we also study the effect of estimation errors on the predictions. In all the cases, we compare the performance of predictions by using predictions based on a bivariate series and predictions based on a univariate series, which allows to illustrate the advantage of the proposed method. For practical matters, we provide a complete example of application on financial data.
Bouvier, Pierre. "Application des copules à la finance de marché". Thèse, 2010. http://www.archipel.uqam.ca/2765/1/D1897.pdf.
Texto completo da fonteGroparu-Cojocaru, Ionica. "A class of bivariate Erlang distributions and ruin probabilities in multivariate risk models". Thèse, 2012. http://hdl.handle.net/1866/8947.
Texto completo da fonteIn this contribution, we introduce a new class of bivariate distributions of Marshall-Olkin type, called bivariate Erlang distributions. The Laplace transform, product moments and conditional densities are derived. Potential applications of bivariate Erlang distributions in life insurance and finance are considered. Further, our research project is devoted to the study of multivariate risk processes, which may be useful in analyzing ruin problems for insurance companies with a portfolio of dependent classes of business. We apply results from the theory of piecewise deterministic Markov processes in order to derive exponential martingales needed to establish computable upper bounds of the ruin probabilities, as their exact expressions are intractable.
Bélisle, Jessica. "Nouvelle loi exponentielle bidimensionnelle basée sur la méthode des chocs comonotones". Thèse, 2020. http://depot-e.uqtr.ca/id/eprint/9405/1/eprint9405.pdf.
Texto completo da fonteCissé, Mamadou Lamine. "De nouveaux estimateurs semi-paramétriques de l'indice de dépendance extrême de queue". Thèse, 2020. http://depot-e.uqtr.ca/id/eprint/9410/1/eprint9410.pdf.
Texto completo da fonte