Mathematical Foundations of Infinite-Dimensional Statistical Models

Mathematical Foundations of Infinite-Dimensional Statistical Models
Author :
Publisher : Cambridge University Press
Total Pages : 706
Release :
ISBN-10 : 9781009022781
ISBN-13 : 1009022784
Rating : 4/5 (784 Downloads)

Book Synopsis Mathematical Foundations of Infinite-Dimensional Statistical Models by : Evarist Giné

Download or read book Mathematical Foundations of Infinite-Dimensional Statistical Models written by Evarist Giné and published by Cambridge University Press. This book was released on 2021-03-25 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Mathematical Foundations of Infinite-Dimensional Statistical Models Related Books

Mathematical Foundations of Infinite-Dimensional Statistical Models
Language: en
Pages: 706
Authors: Evarist Giné
Categories: Mathematics
Type: BOOK - Published: 2021-03-25 - Publisher: Cambridge University Press

GET EBOOK

In nonparametric and high-dimensional statistical models, the classical Gauss–Fisher–Le Cam theory of the optimality of maximum likelihood estimators and Ba
Mathematical Foundations of Infinite-Dimensional Statistical Models
Language: en
Pages: 705
Authors: Evarist Giné
Categories: Mathematics
Type: BOOK - Published: 2015-11-18 - Publisher: Cambridge University Press

GET EBOOK

In nonparametric and high-dimensional statistical models, the classical Gauss-Fisher-Le Cam theory of the optimality of maximum likelihood estimators and Bayesi
Probabilistic Symmetries and Invariance Principles
Language: en
Pages: 536
Authors: Olav Kallenberg
Categories: Mathematics
Type: BOOK - Published: 2005-07-27 - Publisher: Springer Science & Business Media

GET EBOOK

This is the first comprehensive treatment of the three basic symmetries of probability theory—contractability, exchangeability, and rotatability—defined as
Statistical Foundations of Data Science
Language: en
Pages: 942
Authors: Jianqing Fan
Categories: Mathematics
Type: BOOK - Published: 2020-09-21 - Publisher: CRC Press

GET EBOOK

Statistical Foundations of Data Science gives a thorough introduction to commonly used statistical models, contemporary statistical machine learning techniques
High-Dimensional Probability
Language: en
Pages: 299
Authors: Roman Vershynin
Categories: Business & Economics
Type: BOOK - Published: 2018-09-27 - Publisher: Cambridge University Press

GET EBOOK

An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.