Multivariate partially linear single-index models: Bayesian analysis

Abstract

Partially linear single-index models play important roles in advanced non-/semi-parametric statistics due to their generality and flexibility. We generalise these models from univariate response to multivariate responses. A Bayesian method with free-knot spline is used to analyse the proposed models, including the estimation and the prediction, and a Metropolis-within-Gibbs sampler is provided for posterior exploration. We also utilise the partially collapsed idea in our algorithm to speed up the convergence. The proposed models and methods of analysis are demonstrated by simulation studies and are applied to a real data set.

Keywords:

• free-knot spline
• Gibbs sampler
• reversible jump
• single-index model

Acknowledgements

The authors are grateful to the anonymous referees, the Associate Editor and the Editor for valuable suggestions for improving the manuscript.

Funding

Wang's research was supported by the Natural Science Foundation of China [grant number 11471272] and the Natural Science Foundation of Fujian Province of China [grant number 2013J01019].