Готові списки джерел за темами / Quadratic estimates

Добірка наукової літератури з теми "Quadratic estimates"

Автор: Grafiati
Опубліковано: 10 грудня 2022
Оновлено: 28 січня 2023

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Статті в журналах з теми "Quadratic estimates"

1

Golub, Gene H., and Zdeněk Strakoš. "Estimates in quadratic formulas." Numerical Algorithms 8, no. 2 (September 1994): 241–68. http://dx.doi.org/10.1007/bf02142693.

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2

Karel Pravda-Starov. "Subelliptic estimates for quadratic differential operators." American Journal of Mathematics 133, no. 1 (2011): 39–89. http://dx.doi.org/10.1353/ajm.2011.0003.

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3

Zioutas, G., L. Camarinopoulos, and E. Bora Senta. "Robust autoregressive estimates using quadratic programming." European Journal of Operational Research 101, no. 3 (September 1997): 486–98. http://dx.doi.org/10.1016/s0377-2217(96)00190-7.

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4

Petunin, Yu I., and N. P. Tupko. "Theory of quadratic estimates of variance." Ukrainian Mathematical Journal 51, no. 9 (September 1999): 1370–85. http://dx.doi.org/10.1007/bf02593004.

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5

Lieberman, Gary M. "Gradient estimates for semilinear elliptic equations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 100, no. 1-2 (1985): 11–17. http://dx.doi.org/10.1017/s0308210500013597.

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SynopsisEstimates on the gradient of solutions to the Dirichlet problem for a semilinear elliptic equation are given when the nonlinearity in the equation is quadratic with respect to the gradient of the solution. These estimates extend results of F. Tomi to less smooth boundary data and results of the author to the full quadratic growth.
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Severin, Valeriy P. "Automatic Control Systems Integral Quadratic Estimates Minimization. Part 1. Estimates computation." Journal of Automation and Information Sciences 36, no. 7 (2004): 1–11. http://dx.doi.org/10.1615/jautomatinfscien.v36.i7.10.

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Hitrik, Michael, Johannes Sjöstrand, and Joe Viola. "Resolvent estimates for elliptic quadratic differential operators." Analysis & PDE 6, no. 1 (June 1, 2013): 181–96. http://dx.doi.org/10.2140/apde.2013.6.181.

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8

Rotar’, V. I., and T. L. Shervashidze. "Some Estimates of Distributions of Quadratic Forms." Theory of Probability & Its Applications 30, no. 3 (September 1986): 585–90. http://dx.doi.org/10.1137/1130072.

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9

Vieu, Philippe. "Quadratic errors for nonparametric estimates under dependence." Journal of Multivariate Analysis 39, no. 2 (November 1991): 324–47. http://dx.doi.org/10.1016/0047-259x(91)90105-b.

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Henriot, Kevin, and Kevin Hughes. "On Restriction Estimates for Discrete Quadratic Surfaces." International Mathematics Research Notices 2019, no. 23 (February 3, 2018): 7139–59. http://dx.doi.org/10.1093/imrn/rnx255.

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Abstract We obtain truncated restriction estimates of an unexpected form for discrete surfaces $$\begin{align*}S_N = \{\, ( n_1 , \dots , n_d , R( n_1 , \dots, n_d ) ) \,,\, n_i \in [-N,N] \cap {\mathbb{Z}} \,\},\end{align*}$$ where $R$ is an indefinite quadratic form with integer matrix.
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Більше джерел

Дисертації з теми "Quadratic estimates"

1

Feneuil, Joseph. "Analyse harmonique sur les graphes et les groupes de Lie : fonctionnelles quadratiques, transformées de Riesz et espaces de Besov." Thesis, Université Grenoble Alpes (ComUE), 2015. http://www.theses.fr/2015GREAM040/document.

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Ce mémoire est consacré à des résultats d'analyse harmonique réelle dans des cadres géométriques discrets (graphes) ou continus (groupes de Lie).Soit $\Gamma$ un graphe (ensemble de sommets et d'arêtes) muni d'un laplacien discret $\Delta=I-P$, où $P$ est un opérateur de Markov.Sous des hypothèses géométriques convenables sur $\Gamma$, nous montrons la continuité $L^p$ de fonctionnelles de Littlewood-Paley fractionnaires. Nous introduisons des espaces de Hardy $H^1$ de fonctions et de $1$-formes différentielles sur $\Gamma$, dont nous donnons plusieurs caractérisations, en supposant seulement la propriété de doublement pour le volume des boules de $\Gamma$. Nous en déduisons la continuité de la transformée de Riesz sur $H^1$. En supposant de plus des estimations supérieures ponctuelles (gaussiennes ou sous-gaussiennes) sur les itérées du noyau de l'opérateur $P$, nous obtenons aussi la continuité de la transformée de Riesz sur $L^p$ pour $10$, $1\leq p\leq+\infty$ et $1\leq q\leq +\infty$. Les résultats sont valables en croissance polynomiale ou exponentielle du volume des boules
This thesis is devoted to results in real harmonic analysis in discrete (graphs) or continuous (Lie groups) geometric contexts.Let $\Gamma$ be a graph (a set of vertices and edges) equipped with a discrete laplacian $\Delta=I-P$, where $P$ is a Markov operator.Under suitable geometric assumptions on $\Gamma$, we show the $L^p$ boundedness of fractional Littlewood-Paley functionals. We introduce $H^1$ Hardy spaces of functions and of $1$-differential forms on $\Gamma$, giving several characterizations of these spaces, only assuming the doubling property for the volumes of balls in $\Gamma$. As a consequence, we derive the $H^1$ boundedness of the Riesz transform. Assuming furthermore pointwise upper bounds for the kernel (Gaussian of subgaussian upper bounds) on the iterates of the kernel of $P$, we also establish the $L^p$ boundedness of the Riesz transform for $10$, $1\leq p\leq+\infty$ and $1\leq q\leq +\infty$.These results hold for polynomial as well as for exponential volume growth of balls
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Bibinger, Markus. "Estimating the quadratic covariation from asynchronous noisy high-frequency observations." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2011. http://dx.doi.org/10.18452/16365.

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Ein nichtparametrisches Schätzverfahren für die quadratische Kovariation von hochfrequent nicht-synchron beobachteter Itô-Prozessen mit einem additiven Rauschen wird entwickelt. Für eine artverwandte Folge von statistischen Experimenten wird die lokal asymptotische Normalität (LAN) im Sinne von Le Cam bewiesen. Mit dieser lassen sich optimale Konvergenzraten und Effizienzschranken für asymptotische Varianzen ableiten. Der vorgestellte Schätzer wird auf Grundlage von zwei modernen Verfahren, für die Anwendung bei nicht-synchronen Beobachtungen zum einen, und einem additiven Rauschen zum anderen, entwickelt. Der Hayashi-Yoshida Schätzer wird in einer neuen Darstellung eingeführt, welche einen Synchronisierungsalgorithmus mit einschließt, der für die kombinierte Methode ausgelegt werden kann. Es wird eine stabiles zentrales Grenzwerttheorem bewiesen, wobei spezieller Wert auf die Analyse des Einflusses der Nicht-Synchronität auf die asymptotische Varianz gelegt wird. Nach diesen Vorbereitungen wird das kombinierte Schätzverfahren für den allgemeinsten Fall nicht-synchroner verrauschter Beobachtungen vorgestellt. Dieses beruht auf Subsampling- und Multiskalenmethoden, die auf Mykland, Zhang und Aït-Sahalia zurück gehen. Es vereint positive Eigenschaften der beiden Ursprünge. Das zentrale Resultat dieser Arbeit ist der Beweis, dass der Schätzfehler stabil in Verteilung gegen eine gemischte Normalverteilung konvergiert. Für die asymptotische Varianz wird ein konsistenter Schätzer angegeben. In einer Anwendungsstudie wird eine praktische Implementierung des Schätzverfahrens, die die Wahl von abhängigen Parametern beinhaltet, getestet und auf ihre Eigenschaften im Falle endlicher Stichprobenumfänge untersucht. Neuen fortgeschrittenen Entwicklungen auf dem Forschungsfeld von Seite anderer Autoren wird Rechnung getragen durch Vergleiche und diesbezügliche Kommentare.
A nonparametric estimation approach for the quadratic covariation of Itô processes from high-frequency observations with an additive noise is developed. It is proved that a closely related sequence of statistical experiments is locally asymptotically normal (LAN) in the Le Cam sense. By virtue of this property optimal convergence rates and efficiency bounds for asymptotic variances of estimators can be concluded. The proposed nonparametric estimator is founded on a combination of two modern estimation methods devoted to an additive observation noise on the one hand and asynchronous observation schemes on the other hand. We reinvent this Hayashi-Yoshida estimator in a new illustration that can serve as a synchronization method which is possible to adapt for the combined approach. A stable central limit theorem is proved focusing especially on the impact of non-synchronicity on the asymptotic variance. With this preparations on hand, the generalized multiscale estimator for the noisy and asynchronous setting arises. This convenient method for the general model is based on subsampling and multiscale estimation techniques that have been established by Mykland, Zhang and Aït-Sahalia. It preserves valuable features of the synchronization methodology and the estimators to cope with noise perturbation. The central result of the thesis is that the estimation error of the generalized multiscale estimator converges with optimal rate stably in law to a centred mixed normal limiting distribution on fairly general regularity assumptions. For the asymptotic variance a consistent estimator based on time transformed histograms is given making the central limit theorem feasible. In an application study a practicable estimation algorithm including a choice of tuning parameters is tested for its features and finite sample size behaviour. We take account of recent advances on the research field by other authors in comparisons and notes.
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Stocker, Toni Clemens. "On the asymptotic properties of the OLS estimator in regression models with fractionally integrated regressors and errors." [S.l. : s.n.], 2008. http://nbn-resolving.de/urn:nbn:de:bsz:352-opus-57370.

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4

Binard, Carole. "Estimation de fonctions de régression : sélection d'estimateurs ridge, étude de la procédure PLS1 et applications à la modélisation de la signature génique du cancer du poumon." Thesis, Nice, 2016. http://www.theses.fr/2016NICE4015.

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Cette thèse porte sur l’estimation d'une fonction de régression fournissant la meilleure relation entredes variables pour lesquelles on possède un certain nombre d’observations. Une première partie portesur une étude par simulation de deux méthodes automatiques de sélection du paramètre de laprocédure d'estimation ridge. D'un point de vue plus théorique, on présente et compare ensuite deuxméthodes de sélection d'un multiparamètre intervenant dans une procédure d'estimation d'unefonction de régression sur l'intervalle [0,1]. Dans une deuxième partie, on étudie la qualité del'estimateur PLS1, d'un point de vue théorique, à travers son risque quadratique et, plus précisément,le terme de variance dans la décomposition biais/variance de ce risque. Enfin, dans une troisièmepartie, une étude statistique sur données réelles est menée afin de mieux comprendre la signaturegénique de cellules cancéreuses à partir de la signature génique des sous-types cellulaires constituantle stroma tumoral associé
This thesis deals with the estimation of a regression function providing the best relationship betweenvariables for which we have some observations. In a first part, we complete a simulation study fortwo automatic selection methods of the ridge parameter. From a more theoretical point of view, wethen present and compare two selection methods of a multiparameter, that is used in an estimationprocedure of a regression function on [0,1]. In a second part, we study the quality of the PLS1estimator through its quadratic risk and, more precisely, the variance term in its bias/variancedecomposition. In a third part, a statistical study is carried out in order to explain the geneticsignature of cancer cells thanks to the genetic signatures of cellular subtypes which compose theassociated tumor stroma
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5

Haddouche, Mohamed Anis. "Estimation d'une matrice d'échelle." Thesis, Normandie, 2019. http://www.theses.fr/2019NORMR058/document.

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Beaucoup de résultats sur l’estimation d’une matrice d’échelle en analyse multidimensionnelle sont obtenus sous l’hypothèse de normalité (condition sous laquelle il s’agit de la matrice de covariance). Or il s’avère que, dans des domaines tels que la gestion de portefeuille en finance, cette hypothèse n’est pas très appropriée. Dans ce cas, la famille des distributions à symétrie elliptique, qui contient la distribution gaussienne, est une alternative intéressante. Nous considérons dans cette thèse le problème d’estimation de la matrice d’échelle Σ du modèle additif Yp_m = M + E, d’un point de vue de la théorie de la décision. Ici, p représente le nombre de variables, m le nombre d’observations, M une matrice de paramètres inconnus de rang q < p et E un bruit aléatoire de distribution à symétrie elliptique, avec une matrice de covariance proportionnelle à Im x Σ. Ce problème d’estimation est abordé sous la représentation canonique de ce modèle où la matrice d’observation Y est décomposée en deux matrices, à savoir, Zq x p qui résume l’information contenue dans M et une matrice Un x p, où n = m - q, qui résume l’information suffisante pour l’estimation de Σ. Comme les estimateurs naturels de la forme Σa = a S (où S = UT U et a est une constante positive) ne sont pas de bons estimateurs lorsque le nombre de variables p et le rapport p=n sont grands, nous proposons des estimateurs alternatifs de la forme ^Σa;G = a(S + S S+G(Z; S)) où S+ est l’inverse de Moore-Penrose de S (qui coïncide avec l’inverse S-1 lorsque S est inversible). Nous fournissons des conditions sur la matrice de correction SS+G(Z; S) telles que ^Σa;G améliore^Σa sous le coût quadratique L(Σ; ^Σ) = tr(^ΣΣ‾1 - Ip)² et sous une modification de ce dernier, à savoir le coût basé sur les données LS (Σ; ^Σ) = tr(S+Σ(^ΣΣ‾1 - Ip)²). Nous adoptons une approche unifiée des deux cas où S est inversible et S est non inversible. À cette fin, une nouvelle identité de type Stein-Haff et un nouveau calcul sur la décomposition en valeurs propres de S sont développés. Notre théorie est illustrée par une grande classe d’estimateurs orthogonalement invariants et par un ensemble de simulations
Numerous results on the estimation of a scale matrix in multivariate analysis are obtained under Gaussian assumption (condition under which it is the covariance matrix). However in such areas as Portfolio management in finance, this assumption is not well adapted. Thus, the family of elliptical symmetric distribution, which contains the Gaussian distribution, is an interesting alternative. In this thesis, we consider the problem of estimating the scale matrix _ of the additif model Yp_m = M + E, under theoretical decision point of view. Here, p is the number of variables, m is the number of observations, M is a matrix of unknown parameters with rank q < p and E is a random noise, whose distribution is elliptically symmetric with covariance matrix proportional to Im x Σ. It is more convenient to deal with the canonical forme of this model where Y is decomposed in two matrices, namely, Zq_p which summarizes the information contained in M, and Un_p, where n = m - q which summarizes the information sufficient to estimate Σ. As the natural estimators of the form ^Σ a = a S (where S = UT U and a is a positive constant) perform poorly when the dimension of variables p and the ratio p=n are large, we propose estimators of the form ^Σa;G = a(S + S S+G(Z; S)) where S+ is the Moore-Penrose inverse of S (which coincides with S-1 when S is invertible). We provide conditions on the correction matrix SS+G(Z; S) such that ^Σa;G improves over ^Σa under the quadratic loss L(Σ; ^Σ) = tr(^ΣΣ‾1 - Ip)² and under the data based loss LS (Σ; ^Σ) = tr(S+Σ(^ΣΣ‾1 - Ip)²).. We adopt a unified approach of the two cases where S is invertible and S is non-invertible. To this end, a new Stein-Haff type identity and calculus on eigenstructure for S are developed. Our theory is illustrated with the large class of orthogonally invariant estimators and with simulations
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Goffard, Pierre-Olivier. "Approximations polynomiales de densités de probabilité et applications en assurance." Thesis, Aix-Marseille, 2015. http://www.theses.fr/2015AIXM4026/document.

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Cette thèse a pour objet d'étude les méthodes numériques d'approximation de la densité de probabilité associée à des variables aléatoires admettant des distributions composées. Ces variables aléatoires sont couramment utilisées en actuariat pour modéliser le risque supporté par un portefeuille de contrats. En théorie de la ruine, la probabilité de ruine ultime dans le modèle de Poisson composé est égale à la fonction de survie d'une distribution géométrique composée. La méthode numérique proposée consiste en une projection orthogonale de la densité sur une base de polynômes orthogonaux. Ces polynômes sont orthogonaux par rapport à une mesure de probabilité de référence appartenant aux Familles Exponentielles Naturelles Quadratiques. La méthode d'approximation polynomiale est comparée à d'autres méthodes d'approximation de la densité basées sur les moments et la transformée de Laplace de la distribution. L'extension de la méthode en dimension supérieure à $1$ est présentée, ainsi que l'obtention d'un estimateur de la densité à partir de la formule d'approximation. Cette thèse comprend aussi la description d'une méthode d'agrégation adaptée aux portefeuilles de contrats d'assurance vie de type épargne individuelle. La procédure d'agrégation conduit à la construction de model points pour permettre l'évaluation des provisions best estimate dans des temps raisonnables et conformément à la directive européenne Solvabilité II
This PhD thesis studies numerical methods to approximate the probability density function of random variables governed by compound distributions. These random variables are useful in actuarial science to model the risk of a portfolio of contracts. In ruin theory, the probability of ultimate ruin within the compound Poisson ruin model is the survival function of a geometric compound distribution. The proposed method consists in a projection of the probability density function onto an orthogonal polynomial system. These polynomials are orthogonal with respect to a probability measure that belongs to Natural Exponential Families with Quadratic Variance Function. The polynomiam approximation is compared to other numerical methods that recover the probability density function from the knowledge of the moments or the Laplace transform of the distribution. The polynomial method is then extended in a multidimensional setting, along with the probability density estimator derived from the approximation formula. An aggregation procedure adapted to life insurance portfolios is also described. The method aims at building a portfolio of model points in order to compute the best estimate liabilities in a timely manner and in a way that is compliant with the European directive Solvency II
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Gismalla, Yousif Ebtihal. "Performance analysis of spectrum sensing techniques for cognitive radio systems." Thesis, University of Manchester, 2013. https://www.research.manchester.ac.uk/portal/en/theses/performance-analysis-of-spectrum-sensing-techniques-for-cognitive-radio-systems(157fe1af-717c-4705-a649-d809766cf5cb).html.

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Cognitive radio is a technology that aims to maximize the current usage of the licensed frequency spectrum. Cognitive radio aims to provide services for license-exempt users by making use of dynamic spectrum access (DSA) and opportunistic spectrum sharing strategies (OSS). Cognitive radios are defined as intelligent wireless devices capable of adapting their communication parameters in order to operate within underutilized bands while avoiding causing interference to licensed users. An underused band of frequencies in a specific location or time is known as a spectrum hole. Therefore, in order to locate spectrum holes, reliable spectrum sensing algorithms are crucial to facilitate the evolution of cognitive radio networks. Since a large and growing body of literature has mainly focused into the conventional time domain (TD) energy detector, throughout this thesis the problem of spectrum sensing is investigated within the context of a frequency domain (FD) approach. The purpose of this study is to investigate detection based on methods of nonparametric power spectrum estimation. The considered methods are the periodogram, Bartlett's method, Welch overlapped segments averaging (WOSA) and the Multitaper estimator (MTE). Another major motivation is that the MTE is strongly recommended for the application of cognitive radios. This study aims to derive the detector performance measures for each case. Another aim is to investigate and highlight the main differences between the TD and the FD approaches. The performance is addressed for independent and identically distributed (i.i.d.) Rayleigh channels and the general Rician and Nakagami fading channels. For each of the investigated detectors, the analytical models are obtained by studying the characteristics of the Hermitian quadratic form representation of the decision statistic and the matrix of the Hermitian form is identified. The results of the study have revealed the high accuracy of the derived mathematical models. Moreover, it is found that the TD detector differs from the FD detector in a number of aspects. One principal and generalized conclusion is that all the investigated FD methods provide a reduced probability of false alarm when compared with the TD detector. Also, for the case of periodogram, the probability of sensing errors is independent of the length of observations, whereas in time domain the probability of false alarm is increased when the sample size increases. The probability of false alarm is further reduced when diversity reception is employed. Furthermore, compared to the periodogram, both Bartlett method and Welch method provide better performance in terms of lower probability of false alarm but an increased probability of detection for a given probability of false alarm. Also, the performance of both Bartlett's method and WOSA is sensitive to the number of segments, whereas WOSA is also sensitive to the overlapping factor. Finally, the performance of the MTE is dependent on the number of employed discrete prolate spheroidal (Slepian) sequences, and the MTE outperforms the periodogram, Bartlett's method and WOSA, as it provides the minimal probability of false alarm.
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8

Tanguay, Allison J. "New bilinear estimates for quadratic-derivative nonlinear wave equations in 2+1 dimensions." 2012. https://scholarworks.umass.edu/dissertations/AAI3546060.

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This thesis is concerned with the Cauchy problem for the quadratic derivative nonlinear wave equation in two spatial dimensions. Using standard techniques, we reduce local well-posedness in Fourier Lebesgue spaces to bilinear estimates in associated wave Fourier Lebesgue spaces, for which we prove new product estimates. These estimates then allow us to establish local well-posedness in a parameter range that gives improvement over previously known results on the Sobolev scale.
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Morris, Andrew Jordan. "Local Hardy spaces and quadratic estimates for Dirac type operators on Riemannian manifolds." Phd thesis, 2010. http://hdl.handle.net/1885/8864.

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The connection between quadratic estimates and the existence of a bounded holomorphic functional calculus of an operator provides a framework for applying harmonic analysis to the theory of differential operators. This is a generalization of the connection between Littlewood--Paley--Stein estimates and the functional calculus provided by the Fourier transform. We use the former approach in this thesis to study first-order differential operators on Riemannian manifolds. The theory developed is local in the sense that it does not depend on the spectrum of the operator in a neighbourhood of the origin. When we apply harmonic analysis to obtain estimates, the local theory only requires that we do so up to a finite scale. This allows us to consider manifolds with exponential volume growth in situations where the global theory requires polynomial volume growth. A holomorphic functional calculus is constructed for operators on a reflexive Banach space that are bisectorial except possibly in a neighbourhood of the origin. We prove that this functional calculus is bounded if and only if certain local quadratic estimates hold. For operators with spectrum in a neighbourhood of the origin, the results are weaker than those for bisectorial operators. For operators with a spectral gap in a neighbourhood of the origin, the results are stronger. In each case, however, local quadratic estimates are a more appropriate tool than standard quadratic estimates for establishing that the functional calculus is bounded. This theory allows us to define local Hardy spaces of differential forms that are adapted to a class of first-order differential operators on a complete Riemannian manifold with at most exponential volume growth. The local geometric Riesz transform associated with the Hodge--Dirac operator is bounded on these spaces provided that a certain condition on the exponential growth of the manifold is satisfied. A characterisation of these spaces in terms of local molecules is also obtained. These results can be viewed as the localisation of those for the Hardy spaces of differential forms introduced by Auscher, McIntosh and Russ. Finally, we introduce a class of first-order differential operators that act on the trivial bundle over a complete Riemannian manifold with at most exponential volume growth and on which a local Poincar\'{e} inequality holds. A local quadratic estimate is established for certain perturbations of these operators. As an application, we solve the Kato square root problem for divergence form operators on complete Riemannian manifolds with Ricci curvature bounded below that are embedded in Euclidean space with a uniformly bounded second fundamental form. This is based on the framework for Dirac type operators that was introduced by Axelsson, Keith and McIntosh.
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10

Bandara, Lashi. "Geometry and the Kato square root problem." Phd thesis, 2013. http://hdl.handle.net/1885/10690.

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The primary focus of this thesis is to consider Kato square root problems for various divergence-form operators on manifolds. This is the study of perturbations of second-order differential operators by bounded, complex, measurable coefficients. In general, such operators are not self-adjoint but uniformly elliptic. The Kato square root problem is then to understand when the square root of such an operator, which exists due to uniform ellipticity, is comparable to its unperturbed counterpart. A remarkably adaptable operator-theoretic framework due to Axelsson, Keith and McIntosh sits in the background of this work. This framework allows us to take a powerful first-order perspective of the problems which we consider in a geometric setting. Through a well established procedure, we reduce these problems to the study of quadratic estimates. Under a set of natural conditions, we prove quadratic estimates for a class of operators on vector bundles over complete measure metric spaces. The first kind of estimates we prove are global, and we establish them on trivial vector bundles when the underlying measure grows at most polynomially. The second kind are local, and there, we allow the vector bundle to be non-trivial but bounded in an appropriate sense. Here, the measure is allowed to grow exponentially. An important consequence of obtaining quadratic estimates on measure metric spaces is that it allows us to consider subelliptic operators on Lie groups. The first-order perspective allows us to reduce the subelliptic problem to a fully elliptic one on a sub-bundle. As a consequence, we are able to solve a homogeneous Kato square root problem for perturbations of subelliptic operators on nilpotent Lie groups. For general Lie groups we solve a similar inhomogeneous problem. In the situation of complete Riemannian manifolds, we consider uniformly elliptic divergence-form operators arising from connections on vector bundles. Under a set of assumptions, we show that the Kato square root problem can be solved for such operators. As a consequence, we solve this problem on functions under the condition that the Ricci curvature and injectivity radius are bounded. Assuming an additional lower bound for the curvature endomorphism on forms, we solve a similar problem for perturbations of inhomogeneous Hodge-Dirac operators. A theorem for tensors is obtained by additionally assuming boundedness of a second-order Riesz transform. Motivated by the study of these Kato problems, where for technical reasons it is useful to know the density of compactly supported functions in the domains of operators, we study connections and their divergence on a vector bundle. Through a first-order formulation, we show that this density property holds for the domains of these operators if the metric and connection are compatible and the underlying manifold is complete. We also show that compactly supported functions are dense in the second-order Sobolev space on complete manifolds under the sole assumption that the Ricci curvature is bounded below, improving a result that previously required an additional lower bound on the injectivity radius.
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Книги з теми "Quadratic estimates"

1

Elsner, Guido. Distributions of values of indefinite forms and higher-order spectral estimates for finite Markov chains. Bielefeld: [s.n.], 2007.

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2

Elsner, Guido. Distributions of values of indefinite forms and higher-order spectral estimates for finite Markov chains. Bielefeld: [s.n.], 2007.

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3

Isett, Philip. The Coarse Scale Flow and Commutator Estimates. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0016.

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This chapter derives estimates for the coarse scale flow and commutator. Instead of mollifying the velocity field in the time variable, it derives a Transport equation for vsubscript Element and some estimates that will be necessary for the proof. Here the quadratic term arises from the failure of the nonlinearity to commute with the averaging. Commutator estimates are then derived. To observe cancellation in the quadratic term, the control over the higher-frequency part of v is used, and cancellation is obtained from the lower-frequency parts. It becomes clear that the commutator terms can be estimated using the control of only the derivatives of v. The chapter concludes by presenting the theorem for coarse scale flow estimates.
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Sogge, Christopher D. Geodesics and the Hadamard parametrix. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691160757.003.0002.

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This chapter studies the spectrum of Laplace–Beltrami operators on compact manifolds. It begins by defining a metric on an open subset Ω‎ ⊂ Rn, in order to lift their results to corresponding ones on compact manifolds. The chapter then details some elliptic regularity estimates, before embarking on a brief review of geodesics and normal coordinates. The purpose of this review is to show that, with given a particular Laplace–Beltrami operator and any point y0 in Ω‎, one can choose a natural local coordinate system y = κ‎(x) vanishing at y0 so that the quadratic form associated with the metric takes a special form. To conclude, the chapter turns to the Hadamard parametrix.
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5

Cheng, Russell. Non-Standard Problems: Some Examples. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0002.

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This chapter provides motivation for the rest of the book by giving a selection of simple examples showing how non-standard behaviour can occur. The well-known maximum likelihood estimator is used throughout this book to estimate an unknown vector of parameters. Its behaviour is standard if the log-likelihood is a concave quadratic function with the maximum in the neighbourhood of the true parameter value, but is otherwise non-standard. Examples of non-standard situations given in this chapter include the true parameter value not being an internal point of the parameter space, but being on a fixed boundary that may not even be finite, or where the mathematical form of the log-likelihood is different with non-estimable indeterminate parameters, or where the true model is an embedded model. Other examples given include where the log-likelihood is unbounded at a finite parameter point, is discontinuous, or is no longer quadratic.
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Walsh, Bruce, and Michael Lynch. Measuring Multivariate Selection. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198830870.003.0030.

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This chapter extends many of the results from Chapter 29 on single trait-fitness associations to the multiple trait setting. It examines the estimate of multivariate fitness surfaces, starting with quadratic surfaces and then moving to nonparametric versions (which assume no a prior functional form). It also examines path analysis, the analysis of missing data, and multilevel selection.
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7

Anselmi, A. C. M., S. C. E. Gallon, P. Müller, and K. Reinhardt. Populationsgröße, Trichterdichte und Habitatpräferenz der Dünen-Ameisenjungfer Myrmeleon bore (Tjeder, 1941) im Gebiet der Dresdner Heide (Neuroptera). Technische Universität Dresden, 2021. http://dx.doi.org/10.25368/2022.402.

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Following the first record of Myrmeleon bore (Tjeder, 1941) in the Dresden Heath area in 2019 (KURTH 2020, Sächs. Entomol. Z. 10: 71-80), the population size and density of the species was determined. M. bore mainly was found in open, sparsely vegetated, sandy areas with direct sunlight exposure. The area-weighted density of the entire study site (4.05 hectares) was 0.177 larvae/m2. Population size estimates based on random quadrat counts lead to a figure of 4000-7000 individuals - the largest known population of this species. The positive correlation between larval size and pit diameter known for this species from laboratory trials was confirmed at our study site. This correlation may allow researchers to estimate the age structure of wild populations. Given the special responsibility of Germany for the protection of this species and the size of the population, we urge the protection of the site and a prioritisation over other protected species found in the area.
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8

Feasibility of a random quadrat study design to estimate changes in density of Mexican spotted owls. Fort Collins, Colo: U.S. Dept. of Agriculture, Forest Service, Rocky Mountain Forest and Range Experiment Station, 1996.

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9

May, C. A. Feasibility of a random quadrat study design to estimate changes in density of Mexican spotted owls. 1996.

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Частини книг з теми "Quadratic estimates"

1

Biasse, Jean-François, Michael J. Jacobson, and Alan K. Silvester. "Security Estimates for Quadratic Field Based Cryptosystems." In Information Security and Privacy, 233–47. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14081-5_15.

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2

Casas, Eduardo, and Fredi Tröltzsch. "Error Estimates for Linear-Quadratic Elliptic Control Problems." In Analysis and Optimization of Differential Systems, 89–100. Boston, MA: Springer US, 2003. http://dx.doi.org/10.1007/978-0-387-35690-7_10.

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3

Naess, Arvid. "Reliability Estimates by Quadratic Approximation of the Limit State Surface." In Lecture Notes in Engineering, 287–95. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-83279-6_20.

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4

Chen, Yanping, and Wenbin Liu. "A Posteriori Error Estimates for Mixed Finite Elements of a Quadratic Control Problem." In Recent Progress in Computational and Applied PDES, 123–34. Boston, MA: Springer US, 2002. http://dx.doi.org/10.1007/978-1-4615-0113-8_8.

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5

Damgård, Ivan Bjerre, and Gudmund Skovbjerg Frandsen. "An Extended Quadratic Frobenius Primality Test with Average and Worst Case Error Estimates." In Fundamentals of Computation Theory, 118–31. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-45077-1_12.

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6

Delshams, Amadeu, Marina Gonchenko, and Pere Gutiérrez. "A Methodology for Obtaining Asymptotic Estimates for the Exponentially Small Splitting of Separatrices to Whiskered Tori with Quadratic Frequencies." In Trends in Mathematics, 31–37. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22129-8_6.

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7

He, Ran, Baogang Hu, Xiaotong Yuan, and Liang Wang. "M-Estimators and Half-Quadratic Minimization." In SpringerBriefs in Computer Science, 3–11. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-07416-0_2.

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8

Pillonetto, Gianluigi, Tianshi Chen, Alessandro Chiuso, Giuseppe De Nicolao, and Lennart Ljung. "Bias." In Regularized System Identification, 1–15. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-95860-2_1.

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AbstractAdopting a quadratic loss, the performance of an estimator can be measured in terms of its mean squared error which decomposes into a variance and a bias component. This introductory chapter contains two linear regression examples which describe the importance of designing estimators able to well balance these two components. The first example will deal with estimation of the means of independent Gaussians. We will review the classical least squares approach which, at first sight, could appear the most appropriate solution to the problem. Remarkably, we will instead see that this unbiased approach can be dominated by a particular biased estimator, the so-called James–Stein estimator. Within this book, this represents the first example of regularized least squares, an estimator which will play a key role in subsequent chapters. The second example will deal with a classical system identification problem: impulse response estimation. A simple numerical experiment will show how the variance of least squares can be too large, hence leading to unacceptable system reconstructions. The use of an approach, known as ridge regression, will give first simple intuitions on the usefulness of regularization in the system identification scenario.
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9

Adhya, Sumanta, Debanjan Bhattacharjee, and Tathagata Banerjee. "Design Weighted Quadratic Inference Function Estimators of Superpopulation Parameters." In Statistics and its Applications, 155–61. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-1223-6_14.

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10

Zioutas, G. "Quadratic Mixed Integer Programming Models in Minimax Robust Regression Estimators." In Theory and Applications of Recent Robust Methods, 387–400. Basel: Birkhäuser Basel, 2004. http://dx.doi.org/10.1007/978-3-0348-7958-3_34.

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Тези доповідей конференцій з теми "Quadratic estimates"

1

Thomson, David J. "Quadratic–Inverse Estimates Of Autocorrelation." In 2018 IEEE Statistical Signal Processing Workshop (SSP). IEEE, 2018. http://dx.doi.org/10.1109/ssp.2018.8450755.

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2

Zaychikova, Nadezhda Anatolyevna. "ECONOMIC MEANING OF QUADRATIC REGRESSION MODELS COEFFICIENTS ESTIMATES." In Российская наука: актуальные исследования и разработки. Самара: Самарский государственный экономический университет, 2022. http://dx.doi.org/10.46554/russian.science-2022.02-1-79/82.

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3

Chen, Han-fu, and Lei Guo. "Optimal adaptive control and consistent parameter estimates for ARMAX model with quadratic cost." In 1986 25th IEEE Conference on Decision and Control. IEEE, 1986. http://dx.doi.org/10.1109/cdc.1986.267322.

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4

Mohan, Shankar, Youngki Kim, and Anna G. Stefanopoulou. "On Improving Battery State of Charge Estimation Using Bulk Force Measurements." In ASME 2015 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/dscc2015-9966.

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Lithium-ion (Li-ion) batteries undergo physical deformation as their state-of-charge (SOC) changes. The physical deformation causes changes in the pressure (equivalently, force) applied at the end-plates of a constrained battery pack or module. This paper proposes the fusion of bulk force and battery voltage measurements to estimate the SOC in Li-ion battery packs. In this paper, using discrete Linear Quadratic Estimators (dLQEs), the advantage of using force measurements in addition to voltage measurement to improve SOC estimates is quantitatively studied through simulations. It is observed that including force measurements can decrease the mean and standard deviation of SOC estimation error by 50% in some SOC intervals.
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5

Zhang, H. W., and Z. L. Lu. "A priori error estimates of mixed finite element methods for nonlinear quadratic convex optimal control problem." In 2008 5th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE). IEEE, 2008. http://dx.doi.org/10.1109/iceee.2008.4723362.

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6

Lu, Z. L., and Y. P. Chen. "A priori error estimates of mixed methods for quadratic convex optimal control problem governed by nonlinear parabolic equations." In 2009 6th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE 2009). IEEE, 2009. http://dx.doi.org/10.1109/iceee.2009.5393432.

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7

Kuster, Mark. "A Closed-Form Solution for Quadratic Distribution Uncetainty from Containment Limits and Probability." In NCSL International Workshop & Symposium. NCSL International, 2013. http://dx.doi.org/10.51843/wsproceedings.2013.57.

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Metrologists may obtain Type B uncertainties from such engineering estimates as “The error falls within 2 units 50% of the time.” The procedure requires selecting an appropriate distribution and determining its standard deviation in terms of the containment limits and probability. The latest revision of NCSLI Recommended Practice RP-12, “Determining and Reporting Measurement Uncertainty”, provides such equations for the normal, student’s t, quadratic, cosine, triangular, trapezoidal, u-shaped, and utility distributions. This paper summarizes the Type B estimation procedure, presents the previously unknown quadratic distribution solution discovered during RP-12 development for symmetric, asymmetric, and single-sided containment limits, and gives example uses.
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8

Lin, Tsung-Ching, Pei-Yu Shih, Wen-Ku Su, and Trieu-Kien Truong. "On decoding (31, 16, 7) quadratic residue code up to its error correcting capacity with bit-error probability estimates." In SPIE Optical Engineering + Applications, edited by Arun K. Majumdar and Christopher C. Davis. SPIE, 2010. http://dx.doi.org/10.1117/12.861076.

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9

Kaszynski, Martin, and Oliver Sawodny. "A Moving Horizon Based Sensor Fusion and Load Estimation Concept for Driving Profile - Based Operating Strategy Optimization in Hybrid Hydraulic Trucks." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87023.

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In this paper, a moving-horizon based concept for estimating the driving load profile of a hybrid hydraulic truck is proposed. First, a simple model of the hybrid hydraulic drivetrain is given. Based on this model and vehicle data, a sensitivity analysis is performed to determine which (time-varying) model parameters must be known to represent the driving load adequately. As a major contribution of this work, a Moving Horizon Estimation (MHE) scheme is developed to estimate mass and road grade from standard measurement data. Starting from an intuitive nonlinear formulation of the optimization task, the setup is then transformed to a constrained linear quadratic problem. It is shown how additional sensor information can be easily incorporated into the optimization framework to enhance the estimates, since an identifiability analysis shows that the parameters are usually not clearly distinguishable. Finally, it is demonstrated how the estimated load profile can be used to evaluate the fuel savings potential of a hybrid hydraulic truck by computing the fuel optimal operating strategy and comparing it to non-hybrid and rule-based strategies.
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10

Beltracchi, T. J., and G. A. Gabriele. "A RQP Based Method for Estimating Parameter Sensitivity Derivatives." In ASME 1988 Design Technology Conferences. American Society of Mechanical Engineers, 1988. http://dx.doi.org/10.1115/detc1988-0020.

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Abstract Parameter sensitivity analysis is defined as the estimation of changes in the modeling functions and design point due to small changes in the fixed parameters of the formulation. There are currently several methods for estimating parameter sensitivities which either require difficult to obtain second order information, or do not return reliable estimates for the derivatives. This paper presents a new method, based on the use of the recursive quadratic programming method in conjunction with differencing formulas to estimate the parameter sensitivities without the need to calculate second order information. The method is compared to existing methods and is shown to be very competitive in terms of the number of function evaluations required. In terms of accuracy, the method is shown to be equivalent to a modified version of the Kuhn-Tucker method, where the Hessian of the Lagrangian is estimated using the BFS method employed by the RQP algorithm. Initial testing on a test set of known characteristics demonstrates that the method can accurately calculate parameter sensitivities.
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Звіти організацій з теми "Quadratic estimates"

1

Garcia-Bernardo, Javier, and Petr Janský. Profit Shifting of Multinational Corporations Worldwide. Institute of Development Studies, March 2021. http://dx.doi.org/10.19088/ictd.2021.005.

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Multinational corporations (MNCs) avoid taxes by shifting their profits from countries where real activity takes place towards tax havens, depriving governments worldwide of billions of tax revenue. Earlier research investigating the scale and distribution of profit shifting has faced methodological and data challenges, both of which we address. First, we propose a logarithmic function to model the extremely non-linear relationship between the location of profits and tax rates faced by MNCs at those locations – that is, the extreme concentration of profits without corresponding economic activity in a small number of low-tax jurisdictions. We show that the logarithmic model allows for a more accurate identification of profit shifting than linear and quadratic models. Second, we apply the logarithmic model to newly available country-by-country reporting data for large MNCs – this provides information on the activities of large MNCs, including for the first time many low- and lower-middle-income countries. We estimate that MNCs shifted US$1 trillion of profits to tax havens in 2016, which implies approximately US$200-300 billion in tax revenue losses worldwide. MNCs headquartered in the United States and Bermuda are the most aggressive at shifting profits towards tax havens, while MNCs headquartered in India, China, Mexico and South Africa the least. We establish which countries gain and lose most from profit shifting: the Cayman Islands, Luxembourg, Bermuda, Hong Kong and the Netherlands are among the most important tax havens, whereas low- and lower-middle-income countries tend to lose more tax revenue relative to their total tax revenue. Our findings thus support the arguments of low- and lower-middle-income countries that they should be represented on an equal footing during international corporate tax reform debates.
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