Bayesian variants of some classical semiparametric regression techniques

This paper develops new Bayesian methods for semiparametric inference in the partial linear Normal regression model: y=zβ+f(x)+ε where f(.) is an unknown function. These methods draw solely on the Normal linear regression model with natural conjugate prior. Hence, posterior results are available which do not suffer from some problems which plague the existing literature such as computational complexity. Methods for testing parametric regression models against semiparametric alternatives are developed. We discuss how these methods can, at some cost in terms of computational complexity, be extended to other models (e.g. qualitative choice models or those involving censoring or truncation) and provide precise details for a semiparametric probit model. We show how the assumption of Normal errors can easily be relaxed.