Rates of contraction with respect to L2-distance for Bayesian nonparametric regression

作     者：Xie, Fangzheng Jin, Wei Xu, Yanxun 

作者机构：Johns Hopkins Univ Dept Appl Math & Stat Baltimore MD 21218 USA 

出 版 物：《ELECTRONIC JOURNAL OF STATISTICS》 (Electron. J. Stat.)

年 卷 期：2019年第13卷第2期

页      面：3485-3512页

核心收录：

主　　题：Bayesian nonparametric regression block prior finite random series Gaussian splines integrated L-2-distance rate of contraction 

摘      要：We systematically study the rates of contraction with respect to the integrated L-2-distance for Bayesian nonparametric regression in a generic framework, and, notably, without assuming the regression function space to be uniformly bounded. The generic framework is very flexible and can be applied to a wide class of nonparametric prior models. Three non-trivial applications of the framework are provided: The finite random series regression of an alpha-Holder function, with adaptive rates of contraction up to a logarithmic factor;The un-modified block prior regression of an alpha-Sobolev function, with adaptive-and-exact rates of contraction;The Gaussian spline regression of an alpha-Holder function, with near optimal rates of contraction. These applications serve as generalization or complement of their respective results in the literature. Extensions to the fixed-design regression problem and sparse additive models in high dimensions are discussed as well.