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Mathematical Foundations of Infinite-Dimensional Statistical Models: Series Number 40 (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 40) - Softcover
Synopsis
Now in paperback: the new classic on the theory of statistical inference in statistical models with an infinite-dimensional parameter space.
"synopsis" may belong to another edition of this title.
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.
"About this title" may belong to another edition of this title.
- PublisherCambridge University Press
- Publication date2021
- ISBN 10 110899413X
- ISBN 13 9781108994132
- BindingPaperback
- LanguageEnglish
- Number of pages704
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Mathematical Foundations of Infinite-Dimensional Statistical Models
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Mathematical Foundations of Infinite-Dimensional Statistical Models (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 40)
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Mathematical Foundations of Infinite-Dimensional Statistical Models (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 40)
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Mathematical Foundations of Infinite-Dimensional Statistical Models (Paperback)
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Paperback. Condition: new. 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. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. Seller Inventory # 9781108994132
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Mathematical Foundations of Infinite-Dimensional Statistical Models (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 40)
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ISBN 10: 110899413X
ISBN 13: 9781108994132
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Mathematical Foundations of Infinite-Dimensional Statistical Models (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 40)
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ISBN 13: 9781108994132
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