A Partially Linear Model Using a Gaussian Process Prior

Abstract

A partially linear model is a semiparametric regression model that consists of parametric and nonparametric regression components in an additive form. In this article, we propose a partially linear model using a Gaussian process regression approach and consider statistical inference of the proposed model. Based on the proposed model, the estimation procedure is described by posterior distributions of the unknown parameters and model comparisons between parametric representation and semi- and nonparametric representation are explored. Empirical analysis of the proposed model is performed with synthetic data and real data applications.

Keywords:

• Covariance function
• Gaussian process regression
• Marginal likelihoods
• Model comparison
• Partially linear model

Mathematics Subject Classification:

• 62F15; 62G08