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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
Book 29 of 46: Cambridge Series in Statistical and Probabilistic Mathematics
Synopsis
Now in paperback: the new classic on the theory of statistical inference in statistical models with an infinite-dimensional parameter space.
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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.
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Mathematical Foundations of Infinite-Dimensional Statistical Models: Series Number 40 (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 40)
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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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ISBN 10: 110899413X
ISBN 13: 9781108994132
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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
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Mathematical Foundations of Infinite-Dimensional Statistical Models
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Paperback. Condition: New. 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
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Mathematical Foundations of Infinite-Dimensional Statistical Models
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Mathematical Foundations of Infinite-Dimensional Statistical Models: 40 (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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ISBN 13: 9781108994132
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