A Gaussian process regression approach to a single-index model
- Authors
- Choi, Taeryon; Shi, Jian Q.; Wang, Bo
- Issue Date
- 2011
- Publisher
- TAYLOR & FRANCIS LTD
- Keywords
- Gaussian process prior; empirical Bayes Gibbs sampler; marginal likelihood; MAP; posterior consistency; single-index model
- Citation
- JOURNAL OF NONPARAMETRIC STATISTICS, v.23, no.1, pp.21 - 36
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF NONPARAMETRIC STATISTICS
- Volume
- 23
- Number
- 1
- Start Page
- 21
- End Page
- 36
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/115005
- DOI
- 10.1080/10485251003768019
- ISSN
- 1048-5252
- Abstract
- We consider a Gaussian process regression (GPR) approach to analysing a single-index model (SIM) from the Bayesian perspective. Specifically, the unknown link function is assumed to be a Gaussian process a priori and a prior on the index vector is considered based on a simple uniform distribution on the unit sphere. The posterior distributions for the unknown parameters are derived, and the posterior inference of the proposed approach is performed via Markov chain Monte Carlo methods based on them. Particularly, in estimating the hyperparameters, different numerical schemes are implemented: fully Bayesian methods and empirical Bayes methods. Numerical illustration of the proposed approach is also made using simulation data as well as well-known real data. The proposed approach broadens the scope of the applicability of the SIM as well as the GPR. In addition, we discuss the theoretical aspect of the proposed method in terms of posterior consistency.
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Collections - College of Political Science & Economics > Department of Statistics > 1. Journal Articles
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