Weighted local linear CQR for varying-coefficient models with missing covariates

This paper considers composite quantile regression (CQR) estimation and inference for varying-coefficient models with missing covariates. We propose the weighted local linear CQR (WLLCQR) estimators for unknown coefficient function when selection probabilities are known, estimated nonparametrically or parametrically. Theoretical and numerical results demonstrate that the WLLCQR estimators with estimating weights are more efficient than the true weights. Moreover, a goodness-of-fit test based on the WLLCQR fittings is developed to test whether the coefficient functions are actually varying. The finite-sample performance of the proposed methodology is assessed by simulation studies. A real data set is conducted to illustrate our proposed method.