Convergence rates for posterior distributions and adaptive estimation

被引：26

作者：

Huang, TM ^{[1
]}

机构：

[1] Iowa State Univ, Dept Stat, Ames, IA 50011 USA

来源：

ANNALS OF STATISTICS | 2004年 / 32卷 / 04期

关键词：

convergence rate; nonparametric regression; density estimation; Bayesian; adaptive estimation; sieves;

D O I：

10.1214/009053604000000490

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

The goal of this paper is to provide theorems on convergence rates of posterior distributions that can be applied to obtain good convergence rates in the context of density estimation as well as regression. We show how to choose priors so that the posterior distributions converge at the optimal rate without prior knowledge of the degree of smoothness of the density function or the regression function to be estimated.

引用

页码：1556 / 1593

页数：38

共 16 条

[1]

Barron A, 1999, ANN STAT, V27, P536

[2] Risk bounds for model selection via penalization [J].