Nonparametric regression using linear combinations of basis functions

Abstract

This paper discusses a Bayesian approach to nonparametric regression initially proposed by Smith and Kohn (1996. Journal of Econometrics 75: 317-344). In this approach the regression function is represented as a linear combination of basis terms. The basis terms can be univariate or multivariate functions and can include polynomials, natural splines and radial basis functions. A Bayesian hierarchical model is used such that the coefficient of each basis term can be zero with positive prior probability. The presence of basis terms in the model is determined by latent indicator variables. The posterior mean is estimated by Markov chain Monte Carlo simulation because it is computationally intra..