Nonparametric estimation of varying-coefficient single-index models

Abstract

The varying-coefficient single-index model has two distinguishing features: partially linear varying-coefficient functions and a single-index structure. This paper proposes a nonparametric method based on smoothing splines for estimating varying-coefficient functions and an unknown link function. Moreover, the average derivative estimation method is applied to obtain the single-index parameter estimates. For interval inference, Bayesian confidence intervals were obtained based on Bayes models for varying-coefficient functions and the link function. The performance of the proposed method is examined both through simulations and by applying it to Boston housing data.

Keywords:

• Bayesian confidence interval
• penalized likelihood
• single-index
• smoothing splines
• varying-coefficient functions

Acknowledgements

This study is supported by Kangwon National University and by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2010-0021695).