剑桥统计和概率数学系列：无限维统计模型的数学基础 英文原版 Mathematical Foundations of Infinite-Dimensional Statistical Models Evarist Giné

基本信息

Format Paperback | 704 pages

Dimensions 176 x 251 x 36mm | 1,270g

Publication date 13 May 2021

Publisher Cambridge University Press

Language English

Edition Revised

Edition Statement Revised edition

ISBN10 110899413X

ISBN13 9781108994132

页面参数仅供参考，具体以实物为准

书籍简介

在非参数和高维统计模型中，关于Z大似然估计器的Z优性和贝叶斯后验推断的经典高斯-菲舍尔-勒卡姆理论并不适用，在过去的几十年中，新的基础和思想已经被开发出来。本书对无穷维参数空间的统计理论作了连贯的阐述。数学基础包括关于高斯和经验过程理论、近似和小波理论以及函数空间的基本理论的自足的 "小课程"。这类模型的统计推断理论--假设检验、估计和置信集--是在决策理论的Z小化范式中提出的。这包括卷积核和投影估计的基本理论，也包括贝叶斯非参数化和非参数化Z大似然估计。在最后一章，发展了非参数模型的自适应推理理论，包括Lepski方法、小波阈值和自相似函数的自适应推理。荣获2017年PROSE数学奖。

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.

作者简介

埃瓦里斯特·吉恩（1944-2015）是康涅狄格大学数学系主任。吉恩是一位杰出的数学家，从事无限维度的数学统计和概率研究。他著有两本书和100多篇文章。

Evarist Gine (1944-2015) was Head of the Department of Mathematics at the University of Connecticut. Gine was a distinguished mathematician who worked on mathematical statistics and probability in infinite dimensions. He was the author of two books and more than 100 articles. 

理查德·尼克尔是剑桥大学纯数学和数学统计系统计实验室的数学统计学教授。

Richard Nickl is Professor of Mathematical Statistics in the Statistical Laboratory within the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge.