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Auteur : Evarist Giné
Catégorie : Livres anglais et étrangers,Science,Mathematics
Broché : * pages
Éditeur : *
Langue : Français, Anglais

In nonparametric and high-dimensional statistical models, the classical Gauss-Fisher-Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades. This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces. The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, on approximation and wavelet theory, and on the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is then presented within the minimax paradigm of decision theory. This includes the basic theory of convolution kernel and projection estimation, but also Bayesian nonparametrics and nonparametric maximum likelihood estimation. In the final chapter, the theory of adaptive inference in nonparametric models is developed, including Lepski's method, wavelet thresholding, and adaptive inference for self-similar functions.

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Mathematical Foundations of Infinite-Dimensional ~ 1.1 Statistical Sampling Models 1.1 Statistical Sampling Models X : . Seonghyeon Kim Mathematical Foundations of Infinite-Dimensional Statistical Models2018.06.22 13/29Chap.1. 1.2 Gaussian Models 1.2.2 Some Nonparametric Gaussian Models Nonparametric regression model with equally spaced design on [0;1] Yi = f(xi)+ϵi; xi = i n;ϵi i:˘i:d: N(0;˙2); i = 1;:::;n The assumption that the xi are .

Mathematical Foundations of Infinite-Dimensional ~ Mathematical Foundations of Infinite-Dimensional Statistical Models In nonparametric and high-dimensional statistical models, the classical Gauss– Fisher–Le Cam theory of the optimality of maximum likelihood and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades. This book gives a coherent account of the statistical .

Mathematical Foundations of Infinite-Dimensional ~ Mathematical Foundations of In nite-Dimensional Statistical Models Chapter 3.2 Evarist Gin e and Richard Nickl Presenter : Seonghyeon Kim 2018.10.26 Evarist Gin e and Richard Nickl Presenter : Seonghyeon KimMathematical Foundations of In nite-Dimensional Statistical Models Chapter 3.22018.10.26 1 / 22

Mathematical Foundations of Infinite-Dimensional ~ Mathematical Foundations of Infinite-Dimensional Statistical Models Evarist Giné , Richard Nickl In nonparametric and high-dimensional statistical models, the classical Gauss-Fisher-Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades.

Mathematical Foundations of Inﬁnite-Dimensional ~ Mathematical foundations of infinite-dimensional statistical models / Evarist Gine, University of Connecticut, Richard Nickl, University of Cambridge.´ pages cm. – (Cambridge series in statistical and probabilistic mathematics) Includes bibliographical references and index. ISBN 978-1-107-04316-9 (hardback) 1. Nonparametric statistics. 2. Function spaces. I. Nickl, Richard, 1980– II .

Mathematical Foundations of Infinite-Dimensional ~ The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, on approximation and wavelet theory, and on the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is then presented within the minimax paradigm of decision theory. This includes the basic .

Mathematical Foundations of Infinite-Dimensional ~ A great book that describes, in a unique and unified way, the theory of statistical inference in high- or infinite dimensional models. The endorsements by leading experts can only be supported. A must read for anyone who wants to understand the mathematical foundations of statistics in the 21st century.

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Mathematical foundations of infinite-dimensional ~ Mathematical foundations of infinite-dimensional statistical models. In nonparametric and high-dimensional statistical models, the classical Gauss-Fisher-Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades.

Mathematical foundations of infinite-dimensional ~ Get this from a library! Mathematical foundations of infinite-dimensional statistical models. [Evarist Giné; Richard Nickl] -- In nonparametric and high-dimensional statistical models, the classical Gauss-Fisher-Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, .

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Amazon / Mathematical Foundations of Infinite-Dimensional ~ Mathematical Foundations of Infinite-Dimensional Statistical Models (Cambridge Series in Statistical and Probabilistic Mathematics Book 40) (English Edition) [Kindle edition] by Giné, Evarist, Nickl, Richard. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Mathematical Foundations of Infinite .

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Mathematical Foundations of Infinite-Dimensional ~ Mathematical Foundations of Infinite-Dimensional Statistical Models. Evarist Giné and Richard Nickl. Publisher: Cambridge University Press. Publication Date: 2017. Number of Pages: 690. Format: Hardcover. Series: Cambridge Series in Statistical and Probabilistic Mathematics. Price: 99.99. ISBN: 9781107043169. Category: Textbook. MAA Review; Table of Contents; We do not plan to review this .

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