Composite quantile estimation in partially functional linear regression model with randomly censored responses

Abstract

In this paper, we focus on the studying of composite quantile estimation for the partially functional linear regression model with randomly censored responses. Concretely, we adopt the approach of inverse probability weighting to estimate the weights by using the survival distribution function of the censoring variables with the methods of Kaplan–Meier and Breslow as well as local Kaplan-Meier respectively. Then, we construct the weighted composite quantile estimators for the slope function and the scalar parameters of the model. Furthermore, the large sample properties, such as the convergence rates of the estimators for the slope function and scalar parameters as well as the asymptotic distribution of the estimators for the scalar parameters are obtained under some mild conditions. In addition, we propose a computationally simple resampling technique to approximate the distribution of the parametric estimators of the model, and establish the interval estimations for the scalar parameters. Finally, the finite sample performances of the model and the estimation method are illustrated by some simulation studies and a real data analysis, which shows that both the model and the estimation methods are effective.