Mathematical Foundations of Infinite-Dimensional Statistical Models
by Evarist GinéIn 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.
- First published
- 2021
- Publishers
- University of Cambridge ESOL Examinations
Books
Mathematical Foundations of Infinite-Dimensional Statistical Models
Evarist Giné
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.
Gliding Flight
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Inventive, dreamy gieles lives with his father and a flock of geese on a plane-spotters’ campsite next to an airstrip.
Mathematical Foundations of Infinite-Dimensional Statistical Models
Evarist Giné
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.
Staatstragende Arbeitsmedizin
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Concentration inequalities, which express the fact that certain complicated random variables are almost constant, have proven of utmost importance in many areas of probability and statistics.
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