Bayesian spectral analysis models for quantile regression with Dirichlet process mixtures
- Authors
- Jo, Seongil; Roh, Taeyoung; Choi, Taeryon
- Issue Date
- 2-1월-2016
- Publisher
- TAYLOR & FRANCIS LTD
- Keywords
- 62F15; 62G08; shrinkage priors; model comparison; Dirichlet process mixtures; cosine basis; variable selection; Markov chain Monte Carlo; asymmetric Laplace
- Citation
- JOURNAL OF NONPARAMETRIC STATISTICS, v.28, no.1, pp.177 - 206
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF NONPARAMETRIC STATISTICS
- Volume
- 28
- Number
- 1
- Start Page
- 177
- End Page
- 206
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/89842
- DOI
- 10.1080/10485252.2015.1124877
- ISSN
- 1048-5252
- Abstract
- This paper presents a Bayesian analysis of partially linear additive models for quantile regression. We develop a semiparametric Bayesian approach to quantile regression models using a spectral representation of the nonparametric regression functions and the Dirichlet process (DP) mixture for error distribution. We also consider Bayesian variable selection procedures for both parametric and nonparametric components in a partially linear additive model structure based on the Bayesian shrinkage priors via a stochastic search algorithm. Based on the proposed Bayesian semiparametric additive quantile regression model referred to as BSAQ, the Bayesian inference is considered for estimation and model selection. For the posterior computation, we design a simple and efficient Gibbs sampler based on a location-scale mixture of exponential and normal distributions for an asymmetric Laplace distribution, which facilitates the commonly used collapsed Gibbs sampling algorithms for the DP mixture models. Additionally, we discuss the asymptotic property of the sempiparametric quantile regression model in terms of consistency of posterior distribution. Simulation studies and real data application examples illustrate the proposed method and compare it with Bayesian quantile regression methods in the literature.
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