Mathematical Foundations of Infinite-Dimensional Statistical Models

The book provides a comprehensive account of the statistical theory in infinite-dimensional parameter spaces,including hypothesis testing,estimation,and confidence sets. It also covers Bayesian nonparametrics and adaptive inference.

Format: Paperback / softback
Length: 704 pages
Publication date: 25 March 2021
Publisher: Cambridge University Press

In the realm of nonparametric and high-dimensional statistical models, the classical Gauss-Fisher-Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference finds limited applicability. Over the past several decades, a rich tapestry of new foundations and ideas has emerged to address these challenges. This comprehensive book presents a coherent account of the statistical theory in infinite-dimensional parameter spaces. It encompasses a range of mathematical foundations, including self-contained mini-courses on the theory of Gaussian and empirical processes, approximation and wavelet theory, and the fundamental theory of function spaces. Within this framework, the theory of statistical inference is explored, encompassing hypothesis testing, estimation, and confidence sets. This is approached from the minimax paradigm of decision theory, encompassing the basic theory of convolution kernel and projection estimation, as well as Bayesian nonparametrics and nonparametric maximum likelihood estimation. In a concluding chapter, the theory of adaptive inference in nonparametric models is developed, encompassing techniques such as Lepski's method, wavelet thresholding, and adaptive inference for self-similar functions. Recognized with the prestigious 2017 PROSE Award for Mathematics, this book offers a valuable resource for researchers and practitioners in the field.

Weight: 1278g
Dimension: 254 x 177 x 46 (mm)
ISBN-13: 9781108994132
Edition number: Revised ed