Mathematical Foundations of Infinite-Dimensional Statistical Models (Cambridge Series in Statistical and Probabilistic Mathematics Book 40) 1st Edition by Evarist Giné | (PDF) Free Download

Description

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 the 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.

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⭐I ordered one with international shipment. The condition of the book was great.

⭐My rating is for the Kindle version and has nothing to do with the quality of the textbook or its contents, which I find delightful and excellent. In the Kindle math formulas appear dithered, some of them are tiny some huge, in other words a complete disservice to a book that I imagine being elegantly typewritten in its physical version. It is unreadable in the kindle version!

⭐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.

⭐Thank you

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