BAYESIAN ESTIMATION IN SINGLE-INDEX MODELS

Single-index models offer a flexible semiparametric regression frame-work for high-dimensional predictors. Bayesian methods have never been proposed for such models. We develop a Bayesian approach incorporating some frequentist methods: B-splines approximate the link function, the prior on the index vector is Fishervon Mises, and regularization with generalized cross validation is adopted to avoid mer-fitting the link function. A random walk Metropolis algorithm is used to sample from the posterior. Simulation results indicate that our procedure provides some improvement over the best frequentist method available. Two data examples are included.