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Mathematical Foundations of Infinite-Dimensional Statistical Models

Paperback / softback

Main Details

Title Mathematical Foundations of Infinite-Dimensional Statistical Models
Authors and Contributors      By (author) Evarist Gine
By (author) Richard Nickl
SeriesCambridge Series in Statistical and Probabilistic Mathematics
Physical Properties
Format:Paperback / softback
Pages:704
Dimensions(mm): Height 251,Width 176
Category/GenreEconometrics
Calculus and mathematical analysis
Probability and statistics
Signal processing
ISBN/Barcode 9781108994132
ClassificationsDewey:519.54
Audience
Professional & Vocational
Edition Revised edition
Illustrations Worked examples or Exercises

Publishing Details

Publisher Cambridge University Press
Imprint Cambridge University Press
Publication Date 25 March 2021
Publication Country United Kingdom

Description

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.

Author Biography

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.