Mathematical Foundations of Infinite-Dimensional Statistical Models

Evarist Giné (u. a.)

ISBN 10: 110899413X / ISBN 13: 9781108994132

Published by Cambridge University Press, 2021

About this Item

Mathematical Foundations of Infinite-Dimensional Statistical Models | Evarist Giné (u. a.) | Taschenbuch | Kartoniert / Broschiert | Englisch | 2021 | Cambridge University Press | EAN 9781108994132 | Verantwortliche Person für die EU: Libri GmbH, Europaallee 1, 36244 Bad Hersfeld, gpsr[at]libri[dot]de | Anbieter: preigu Print on Demand.

Seller Inventory # 119552308

Bibliographic Details

• Title: Mathematical Foundations of Infinite-Dimensional Statistical Models
• Publisher: Cambridge University Press
• Publication Date: 2021
• Language: English
• ISBN 10: 110899413X
• ISBN 13: 9781108994132
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 254W x 178H x 38D millimeters 254 millimeters width by 178 millimeters height by 38 millimeters depth
• Weight: 1304 grams
• Seller catalogs:
  • Bücher

About this title

Synopsis

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.

About the Authors

Evarist Giné (1944–2015) was Head of the Department of Mathematics at the University of Connecticut. Giné 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.