Mathematical Foundations of Infinite-Dimensional Statistical Models
Language: English
Published by Cambridge University Press, GB, 2021
Series: Book 44 of 64 - Cambridge Series in Statistical and Probabilistic Mathematics
- Softcover
- New
Seller: Rarewaves.com UK, London, United KingdomRarewaves.com UK
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Condition: New
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Add to basketItem description from seller
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. …
Seller Inventory # LU-9781108994132
- Title
- Mathematical Foundations of Infinite-Dimensional Statistical Models
- Author
- Richard Nickl, Evarist Giné
- Publisher
- Cambridge University Press, GB
- Publication year
- 2021
- Condition
- New
- Binding
- Paperback
- Language
- English
- ISBN 10
- 110899413X
- ISBN 13
- 9781108994132
- Item weight
- 1,270 grams
- Dimensions
- 17.78 x 4.04 x 25.4 cm
- Series
- Book 44 of 64: Cambridge Series in Statistical and Probabilistic Mathematics
"Synopsis" may belong to another edition of this title.
About the Author
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 the title" may belong to another edition of this title.
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