Bayesian estimation in single-index models. (English) Zbl 1060.62031

Summary: Single-index models offer a flexible semiparametric regression framework 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 Fisher-von Mises, and regularization with generalized cross validation is adopted to avoid over-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 methods available. Two data examples are included.


62F15 Bayesian inference
62G08 Nonparametric regression and quantile regression
65C40 Numerical analysis or methods applied to Markov chains