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Littérature scientifique sur le sujet « Processus stationnaire multivarié »
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Articles de revues sur le sujet "Processus stationnaire multivarié"
Harel, Michel, et Echarif Elharfaoui. « La convergence faible des U-statistiques multivariées pour des processus non stationnaires ». Comptes Rendus Mathematique 337, no 12 (décembre 2003) : 801–4. http://dx.doi.org/10.1016/j.crma.2003.09.034.
Texte intégralThèses sur le sujet "Processus stationnaire multivarié"
Boulin, Alexis. « Partitionnement des variables de séries temporelles multivariées selon la dépendance de leurs extrêmes ». Electronic Thesis or Diss., Université Côte d'Azur, 2024. http://www.theses.fr/2024COAZ5039.
Texte intégralIn a wide range of applications, from climate science to finance, extreme events with a non-negligible probability can occur, leading to disastrous consequences. Extremes in climatic events such as wind, temperature, and precipitation can profoundly impact humans and ecosystems, resulting in events like floods, landslides, or heatwaves. When the focus is on studying variables measured over time at numerous specific locations, such as the previously mentioned variables, partitioning these variables becomes essential to summarize and visualize spatial trends, which is crucial in the study of extreme events. This thesis explores several models and methods for partitioning the variables of a multivariate stationary process, focusing on extreme dependencies.Chapter 1 introduces the concepts of modeling dependence through copulas, which are fundamental for extreme dependence. The notion of regular variation, essential for studying extremes, is introduced, and weakly dependent processes are discussed. Partitioning is examined through the paradigms of separation-proximity and model-based clustering. Non-asymptotic analysis is also addressed to evaluate our methods in fixed dimensions.Chapter 2 study the dependence between maximum values is crucial for risk analysis. Using the extreme value copula function and the madogram, this chapter focuses on non-parametric estimation with missing data. A functional central limit theorem is established, demonstrating the convergence of the madogram to a tight Gaussian process. Formulas for asymptotic variance are presented, illustrated by a numerical study.Chapter 3 proposes asymptotically independent block (AI-block) models for partitioning variables, defining clusters based on the independence of maxima. An algorithm is introduced to recover clusters without specifying their number in advance. Theoretical efficiency of the algorithm is demonstrated, and a data-driven parameter selection method is proposed. The method is applied to neuroscience and environmental data, showcasing its potential.Chapter 4 adapts partitioning techniques to analyze composite extreme events in European climate data. Sub-regions with dependencies in extreme precipitation and wind speed are identified using ERA5 data from 1979 to 2022. The obtained clusters are spatially concentrated, offering a deep understanding of the regional distribution of extremes. The proposed methods efficiently reduce data size while extracting critical information on extreme events.Chapter 5 proposes a new estimation method for matrices in a latent factor linear model, where each component of a random vector is expressed by a linear equation with factors and noise. Unlike classical approaches based on joint normality, we assume factors are distributed according to standard Fréchet distributions, allowing a better description of extreme dependence. An estimation method is proposed, ensuring a unique solution under certain conditions. An adaptive upper bound for the estimator is provided, adaptable to dimension and the number of factors
Elharfaoui, Echarif. « La convergence faible des U-statistiques multivariées pour des processus non stationnaires dépendants ». Toulouse 3, 2003. http://www.theses.fr/2003TOU30144.
Texte intégralPoignard, Benjamin. « Approches nouvelles des modèles GARCH multivariés en grande dimension ». Thesis, Paris Sciences et Lettres (ComUE), 2017. http://www.theses.fr/2017PSLED010/document.
Texte intégralThis document contributes to high-dimensional statistics for multivariate GARCH processes. First, the author proposes a new dynamic called vine-GARCH for correlation processes parameterized by an undirected graph called vine. The proposed approach directly specifies positive definite matrices and fosters parsimony. The author provides results for the existence and uniqueness of stationary solution of the vine-GARCH model and studies its asymptotic properties. He then proposes a general framework for penalized M-estimators with dependent processes and focuses on the asymptotic properties of the adaptive Sparse Group Lasso regularizer. The high-dimensionality setting is studied when considering a diverging number of parameters with the sample size. The asymptotic properties are illustrated through simulation experiments. Finally, the author proposes to foster sparsity for multivariate variance covariance matrix processes within the latter framework. To do so, the multivariate ARCH family is considered and the corresponding parameterizations are estimated thanks to penalized ordinary least square procedures
Livres sur le sujet "Processus stationnaire multivarié"
Benslama, Djaffar. Extrêmes de processus stationnaires gaussiens multivariés. Grenoble : A.N.R.T, Université Pierre Mendes France (Grenoble II), 1986.
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