Mathematical Foundations of Infinite-Dimensional Statistical Models

Evarist Giné, Richard Nickl (University of Cambridge)

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English

Cambridge University Press
25 March 2021

Econometrics; Mathematics & Sciences; Calculus & mathematical analysis; Probability & statistics; Machine learning; Signal processing

Series: Cambridge Series in Statistical and Probabilistic Mathematics

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.

By: Evarist Giné, Richard Nickl (University of Cambridge)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Edition: Revised edition
Dimensions: Height: 251mm, Width: 176mm, Spine: 36mm
Weight: 1.270kg
ISBN: 9781108994132
ISBN 10: 110899413X
Series: Cambridge Series in Statistical and Probabilistic Mathematics
Pages: 704
Publication Date: 25 March 2021
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Evarist Gine (1944-2015) was Head of the Department of Mathematics at the University of Connecticut. Gine 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.