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This paper is concerned with composite quantile regression for partially linear varying-coefficient models with heteroscedasticity when data are right censored and censoring indicators are missing at random. We construct estimators of parametric regression coefficients and nonparametric varying-coefficient functions in the proposed models based on regression calibration, imputation and inverse probability weighted approaches. The asymptotic normality of the proposed estimators is proved. Meanwhile, an adaptive LASSO penalized variable selection method and its oracle property are considered. We also demonstrate the performance of the proposed estimation method and variable selection procedure through comprehensive simulations and a real-data application.

Composite quantile regression for heteroscedastic partially linear varying-coefficient models with missing censoring indicators