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Mathematical Foundations of Infinite-Dimensional Statistical Models (Cambridge Series in Statistical and Probabilistic Mathematics), by Ev
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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, on approximation and wavelet theory, and on the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is then 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.
- Sales Rank: #145091 in Books
- Published on: 2015-11-18
- Original language: English
- Number of items: 1
- Dimensions: 9.96" h x 1.77" w x 6.97" l, .0 pounds
- Binding: Hardcover
- 720 pages
Most helpful customer reviews
4 of 4 people found the following review helpful.
excellent book
By Hanslick, E.
A great book that describes, in a unique and unified way, the theory of statistical inference in high- or infinite dimensional models. The endorsements by leading experts can only be supported. A must read for anyone who wants to understand the mathematical foundations of statistics in the 21st century.
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