Empirical likelihood and estimation in a partially linear varying coefficient model with right censored data

Abstract

In this paper, we study the empirical likelihood and estimation of parameters of interest in a partially linear varying coefficient model with right censored data. Two cases are considered: censoring is independent of the covariates, and censoring depends on the covariates. The bias-corrected empirical log-likelihood ratios for the regression parameters are presented, Wilks' theorem is proved, and thus the confidence regions of the regression parameters are constructed. The estimators of parametric and nonparametric components are constructed, their asymptotic distributions are obtained, and the consistent estimators of the asymptotic variances are also given. Furthermore, the partial profile empirical log-likelihood ratios for each component of the regression parameters and the coefficient functions are constructed, and show they are asymptotically chi-squared. The obtained results can be directly used to construct the confidence regions/intervals for the regression parameters and the pointwise confidence intervals for the coefficient functions. Our approach is to directly calibrate the empirical log-likelihood ratio so that the resulting ratio is asymptotically chi-squared, undersmoothing of the coefficient functions is avoided, and existing data-driven methods can be effectively used to select the optimal bandwidth. Simulation studies compare the empirical likelihood method with one based on normal approximation and perform real data analysis.

Keywords:

• Empirical likelihood
• partially linear varying coefficient model
• right censored data
• regression parameter
• confidence region

Acknowledgments

The author thanks Editor, Associate Editor and two expert referees for their constructive comments and suggestions which improved the presentation of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

The research was supported by the National Natural Science Foundation of China [11971001].