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

Gin�, Evarist

ISBN 10: 110899413X ISBN 13: 9781108994132

Editorial: Cambridge University Press, 2021

Idioma: Ingl�s

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T�tulo

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

Editor

Cambridge University Press

Fecha de publicaci�n

2021

Idioma

Ingl�s

ISBN 10

110899413X

ISBN 13

9781108994132

Encuadernaci�n

Encuadernaci�n de tapa blanda

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New

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Sinopsis

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, approximation and wavelet theory, and the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is 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 a 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. Winner of the 2017 PROSE Award for Mathematics.

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Evarist Gin� (1944–2015) was Head of the Department of Mathematics at the University of Connecticut. Gin� was a distinguished mathematician who worked on mathematical statistics and probability in infinite dimensions. He was the author of two books and more than 100 articles.

Richard Nickl is Professor of Mathematical Statistics in the Statistical Laboratory within the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge.

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