Nonparametric Goodness of Fit via Cross-Validation Bayes Factors

被引：1

作者：

Hart, Jeffrey D. ^{[1
]}

Choi, Taeryon ^{[2
]}

机构：

[1] Texas A&M Univ, Dept Stat, College Stn, TX 77843 USA

[2] Korea Univ, Dept Stat, Seoul, South Korea

来源：

BAYESIAN ANALYSIS | 2017年 / 12卷 / 03期

基金：

新加坡国家研究基金会;

关键词：

bandwidth selection; Bayes factor; consistency; cross validation; goodness-of-fit tests; kernel density estimates; PLANETARY-NEBULAE; STANDARD CANDLES; MODEL;

D O I：

10.1214/16-BA1018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A nonparametric Bayes procedure is proposed for testing the fit of a parametric model for a distribution. Alternatives to the parametric model are kernel density estimates. Data splitting makes it possible to use kernel estimates for this purpose in a Bayesian setting. A kernel estimate indexed by bandwidth is computed from one part of the data, a training set, and then used as a model for the rest of the data, a validation set. A Bayes factor is calculated from the validation set by comparing the marginal for the kernel model with the marginal for the parametric model of interest. A simulation study is used to investigate how large the training set should be, and examples involving astronomy and wind data are provided. A proof of Bayes consistency of the proposed test is also provided.

引用

页码：653 / 677

页数：25

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