A Bayesian Approach to Robust Binary Nonparametric Regression

Abstract

This article presents a Bayesian approach to binary nonparametric regression that assumes that the argument of the link is an additive function of the explanatory variables and their multiplicative interactions. The article makes the following contributions. First, a comprehensive approach is presented in which the function estimates are smoothing splines with the smoothing parameters integrated out and the estimates are made robust to outliers. Second, the approach can handle a wide range of link functions. Third, efficient state-space-based algorithms are used to carry out the computations. Fourth, an extensive set of simulations is carried out, which show that the Bayesian estimator works well and compares favorably to two estimators that have recently been proposed and used in practice.

Key Words:

• Data augmentation
• Gibbs sampler
• Mixture of normals
• State-space model