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On asymptotic properties of Bayesian partially linear models

Authors
Choi, TaeryonWoo, Yoonsung
Issue Date
12월-2013
Publisher
KOREAN STATISTICAL SOC
Keywords
Bayes factor consistency; Gaussian process priors; Dirichlet process mixture; Marginal distribution; Posterior consistency; RKHS
Citation
JOURNAL OF THE KOREAN STATISTICAL SOCIETY, v.42, no.4, pp.529 - 541
Indexed
SCIE
SCOPUS
KCI
Journal Title
JOURNAL OF THE KOREAN STATISTICAL SOCIETY
Volume
42
Number
4
Start Page
529
End Page
541
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/101376
DOI
10.1016/j.jkss.2013.03.003
ISSN
1226-3192
Abstract
In this paper, we present large sample properties of a partially linear model from the Bayesian perspective, in which responses are explained by the semiparametric regression model with the additive form of the linear component and the nonparametric component. For this purpose, we investigate asymptotic behaviors of posterior distributions in terms of consistency. Specifically, we deal with a specific Bayesian partially linear regression model with additive noises in which the nonparametric component is modeled using Gaussian process priors. Under the Bayesian partially linear model using Gaussian process priors, we focus on consistency of posterior distribution and consistency of the Bayes factor, and extend these results to generalized additive regression models and study their asymptotic properties. In addition we illustrate the asymptotic properties based on empirical analysis through simulation studies. (C) 2013 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.
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Choi, Tae ryon
정경대학 (통계학과)
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