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 = z*beta + f(x) + epsilon, where f(.) is an unknown function. These methods draw solely on the Normal linear regression model with natural conjugate prior. Hence, analytical finite sample results are available which do not suffer from problems of theoretical and computational complexity which plague the existing literature. Constrained and unconstrained estimation are considered as is testing of parametric regression models against semiparametric alternatives and prediction. 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 semiparametric probit and tobit models. We show how the assumption of Normal errors can easily be relaxed. Our methods are illustrated using artificial and real data sets.