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A Gaussian process regression approach to a single-index model

Lookup NU author(s): Dr Jian Shi, Dr Bo Wang

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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.

Publication metadata

Author(s): Choi T, Shi JQ, Wang B

Publication type: Article

Publication status: Published

Journal: Journal of Nonparametric Statistics

Year: 2011

Volume: 23

Issue: 1

Pages: 21-36

Print publication date: 10/06/2011

ISSN (print): 1048-5252

ISSN (electronic): 1026-7654

Publisher: Taylor & Francis

URL: http://dx.doi.org/10.1080/10485251003768019

DOI: 10.1080/10485251003768019

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