Mathematical Foundations of Infinite-Dimensional Statistical Models: 40 (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 40) - Tapa dura

Gin�, Evarist; Nickl, Richard

9781107043169: Mathematical Foundations of Infinite-Dimensional Statistical Models: 40 (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 40)

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ISBN 10: 1107043166 ISBN 13: 9781107043169

Editorial: Cambridge University Press, 2016

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High-dimensional and nonparametric statistical models are ubiquitous in modern data science. This book develops a mathematically coherent and objective approach to statistical inference in such models, with a focus on function estimation problems arising from random samples (density estimation) or from Gaussian regression/signal in white noise problems.

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Cr�ticas

'Finally - a book that goes all the way in the mathematics of nonparametric statistics. It is reasonably self-contained, despite its depth and breadth, including accessible overviews of the necessary analysis and approximation theory.' Aad van der Vaart, Universiteit Leiden

'This remarkable book provides a detailed account of a great wealth of mathematical ideas and tools that are crucial in modern statistical inference, including Gaussian and empirical processes (where the first author, Evarist Gin�, was one of the key contributors), concentration inequalities and methods of approximation theory. Building upon these ideas, the authors develop and discuss a broad spectrum of statistical applications such as minimax lower bounds and adaptive inference, nonparametric likelihood methods and Bayesian nonparametrics. The book will be exceptionally useful for a great number of researchers interested in nonparametric problems in statistics and machine learning, including graduate students.' Vladimir Koltchinskii, Georgia Institute of Technology

'This is a very welcome contribution. The wealth of material on the empirical processes and nonparametric statistics is quite exceptional. It is a masterly written treatise offering an unprecedented coverage of the classical theory of nonparametric inference, with glimpses into advanced research topics. For the first time in the monographic literature, estimation, testing and confidence sets are treated in a unified way from the nonparametric perspective with a comprehensive insight into adaptation issues. A delightful major reading that I warmly recommend to anyone wanting to explore the mathematical foundations of these fields.' Alexandre Tsybakov, ENSAE ParisTech

'This is a remarkably comprehensive, detailed and rigorous treatment of mathematical theory for non-parametric and high-dimensional statistics. Special emphasis is on density and regression estimation and corresponding confidence sets and hypothesis testing. The minimax paradigm and adaptivity play a key role.' Natalie Neumeyer, MathSciNet

Rese�a del editor

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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EditorialCambridge University Press
A�o de publicaci�n2016
ISBN 10 1107043166
ISBN 13 9781107043169
Encuadernaci�nTapa dura
IdiomaIngl�s
N�mero de p�ginas720

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Mathematical Foundations of Infinite-Dimensional Statistical Models (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 40)

Gin�, Evarist; Nickl, Richard

Publicado por Cambridge University Press, 2015

ISBN 10: 1107043166 ISBN 13: 9781107043169

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Mathematical Foundations of Infinite-Dimensional Statistical Models (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 40)

Gin�, Evarist; Nickl, Richard

Publicado por Cambridge University Press, 2015

ISBN 10: 1107043166 ISBN 13: 9781107043169

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Mathematical Foundations of Infinite-Dimensional Statistical Models

Gin�, Evarist; Nickl, Richard

Publicado por Cambridge University Press, 2015

ISBN 10: 1107043166 ISBN 13: 9781107043169

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Mathematical Foundations of In

Gin�, Evarist

Publicado por Cambridge University Press, 2015

ISBN 10: 1107043166 ISBN 13: 9781107043169

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Mathematical Foundations of Infinite-Dimensional Statistical Models (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 40)

Gin�, Evarist; Nickl, Richard

Publicado por Cambridge University Press, 2015

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Mathematical Foundations of Infinite-Dimensional Statistical Models

Gin�, Evarist; Nickl, Richard

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Mathematical Foundations of Infinite-dimensional Statistical Models (Hardcover)

Evarist Gine

Publicado por Cambridge University Press, Cambridge, 2015

ISBN 10: 1107043166 ISBN 13: 9781107043169

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Hardcover. Condici�n: new. Hardcover. 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. High-dimensional and nonparametric statistical models are ubiquitous in modern data science. This book develops a mathematically coherent and objective approach to statistical inference in such models, with a focus on function estimation problems arising from random samples (density estimation) or from Gaussian regression/signal in white noise problems. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. N� de ref. del art�culo: 9781107043169

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Mathematical Foundations of Infinite-dimensional Statistical Models

Gin�, Evarist/ Nickl, Richard

Publicado por Cambridge Univ Pr, 2016

ISBN 10: 1107043166 ISBN 13: 9781107043169

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Hardcover. Condici�n: Brand New. 1st edition. 720 pages. 10.37x7.04x1.71 inches. In Stock. This item is printed on demand. N� de ref. del art�culo: __1107043166

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