Mathematical Foundations Of Infinitedimensional Statistical Models 1 Revised Edition Evarist Gin by Evarist Giné, Richard Nickl 9781108994132, 9781009022811, 9781107043169, 110899413X, 1009022814, 1107043166 instant download after payment.

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.

Postscript (2020) • In this paperback edition a large number of (mostly minor) corrections have been incorporated. I would like to thank the various readers and students, specifically Kweku Abraham, who pointed them out to me.