A new local estimation method for single index models for longitudinal data

Abstract

Single index models are natural extensions of linear models and overcome the so-called curse of dimensionality. They are very useful for longitudinal data analysis. In this paper, we develop a new efficient estimation procedure for single index models with longitudinal data, based on Cholesky decomposition and local linear smoothing method. Asymptotic normality for the proposed estimators of both the parametric and nonparametric parts will be established. Monte Carlo simulation studies show excellent finite sample performance. Furthermore, we illustrate our methods with a real data example.

Keywords:

• single index models
• Cholesky decomposition
• local linear regression
• longitudinaldata

AMS Subject Classifications:

• Primary: 62G05
• Secondary: 62E20

Acknowledgments

We sincerely thank the associate editor and two referees for their valuable comments that have led to a greatly improved presentation of our work. We also thank Fresenius Medical Care North America for providing CKD registry data and their collaboration in this analysis.

Disclosure statement

No potential conflict of interest was reported by the authors.