Weighted quantile average estimation for general linear models with missing covariates

We develop a weighted quantile average estimation technique for general linear models with missing covariates. The proposed method is based on optimally combining information over different quantiles via multiple quantile regressions. We establish asymptotic normality of the weighted quantile average estimators when selection probabilities are known, estimated non parametrically and estimated parametrically, respectively. Moreover, we compute optimal weights by minimizing asymptotic variance and then obtain the corresponding optimal weighted quantile average estimates, whose asymptotic variance approaches the Cramer-Rao lower bound under appropriate conditions. Numerical studies and a real data analysis are conducted to investigate the finite sample performance of the proposed method.