Semi-Functional Partial Linear Quantile Regression Model with Randomly Censored Responses

Censored data with functional predictors often emerge in many fields such as biology, neurosciences and so on. Many efforts on functional data analysis (FDA) have been made by statisticians to effectively handle such data. Apart from mean-based regression, quantile regression is also a frequently used technique to fit sample data. To combine the strengths of quantile regression and classical FDA models and to reveal the effect of the functional explanatory variable along with nonfunctional predictors on randomly censored responses, the focus of this paper is to investigate the semi-functional partial linear quantile regression model for data with right censored responses. An inverse-censoring-probability-weighted three-step estimation procedure is proposed to estimate parametric coefficients and the nonparametric regression operator in this model. Under some mild conditions, we also verify the asymptotic normality of estimators of regression coefficients and the convergence rate of the proposed estimator for the nonparametric component. A simulation study and a real data analysis are carried out to illustrate the finite sample performances of the estimators.