Mathematical Foundations of Infinite-dimensional Statistical Models

'Finally - a book that goes all the way in the mathematics of nonparametric statistics. It is reasonably self-contained, despite its depth and breadth, including accessible overviews of the necessary analysis and approximation theory.' Aad van der Vaart, Universiteit Leiden

'This remarkable book provides a detailed account of a great wealth of mathematical ideas and tools that are crucial in modern statistical inference, including Gaussian and empirical processes (where the first author, Evarist Giné, was one of the key contributors), concentration inequalities and methods of approximation theory. Building upon these ideas, the authors develop and discuss a broad spectrum of statistical applications such as minimax lower bounds and adaptive inference, nonparametric likelihood methods and Bayesian nonparametrics. The book will be exceptionally useful for a great number of researchers interested in nonparametric problems in statistics and machine learning, including graduate students.' Vladimir Koltchinskii, Georgia Institute of Technology

'This is a very welcome contribution. The wealth of material on the empirical processes and nonparametric statistics is quite exceptional. It is a masterly written treatise offering an unprecedented coverage of the classical theory of nonparametric inference, with glimpses into advanced research topics. For the first time in the monographic literature, estimation, testing and confidence sets are treated in a unified way from the nonparametric perspective with a comprehensive insight into adaptation issues. A delightful major reading that I warmly recommend to anyone wanting to explore the mathematical foundations of these fields.' Alexandre Tsybakov, ENSAE ParisTech

'This is a remarkably comprehensive, detailed and rigorous treatment of mathematical theory for non-parametric and high-dimensional statistics. Special emphasis is on density and regression estimation and corresponding confidence sets and hypothesis testing. The minimax paradigm and adaptivity play a key role.' Natalie Neumeyer, MathSciNet