文章基本信息

标题：Rates of contraction with respect to $L_{2}$-distance for Bayesian nonparametric regression
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作者：Fangzheng Xie ; Wei Jin ; Yanxun Xu 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2019
卷号：13
期号：2
页码：3485-3512
DOI：10.1214/19-EJS1616
语种：English
出版社：Institute of Mathematical Statistics
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 $\alpha$-Hölder 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 $\alpha$-Hölder 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.
关键词：Bayesian nonparametric regression; block prior; finite random series; Gaussian splines; integrated $L_{2}$-distance; rate of contraction