Mathematical Foundations of Infinite-Dimensional Statistical Models (Paperback)

Language: English

Published by Cambridge University Press, Cambridge, 2021

110899413X / 9781108994132

Series: Book 44 of 64 - Cambridge Series in Statistical and Probabilistic Mathematics

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Paperback. In nonparametric and high-dimensional statistical models, the classical GaussFisherLe 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. 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 or from Gaussian regression/signal in white noise problems. This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.

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Title
Mathematical Foundations of Infinite-Dimensional Statistical Models (Paperback)
Author
Richard Nickl
Publisher
Cambridge University Press, Cambridge
Publication year
2021
Condition
new
Binding
Paperback
Language
English
ISBN 10
110899413X
ISBN 13
9781108994132
Series
Book 44 of 64: Cambridge Series in Statistical and Probabilistic Mathematics

CitiRetail

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