Smoothing Spline Estimation for Partially Linear Single-index Models

Abstract

In this article, the partially linear single-index models are discussed based on smoothing spline and average derivative estimation method. This proposed technique consists of two stages: one is to estimate the vector parameter in the linear part using the smoothing cubic spline method, simultaneously, obtaining the estimator of unknown single-index function; the other is to estimate the single-index coefficients in the single-index part by the using average derivative estimator procedure. Some simulated and real examples are presented to illustrate the performance of this method.

Keywords:

• Average derivative estimate
• Partially linear single-index models
• Smoothing spline

Mathematics Subject Classification:

• Primary 62F10
• Secondary 62G05

Acknowledgments

The research was supported in part by National Natural Science Foundation of China (10871072), Doctoral Fund of Ministry of Education of China (20090076110001), Shanxi's Natural Science Foundation of China (2007011014).