Statistica Sinica 14(2004), 1147-1164

BAYESIAN ESTIMATION IN SINGLE-INDEX MODELS

Anestis Antoniadis$^1$, Gérard Grégoire$^1$ and Ian W. McKeague$^2$

$^1$Université Joseph Fourier and $^2$Columbia University

Abstract: 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 method available. Two data examples are included.

Key words and phrases: B-splines, Fisher-von Mises, projection pursuit regression, random walk Metropolis.