A Convex Programming Solution Based Debiased Estimator for Quantile with Missing Response and High-dimensional Covariables

This paper is concerned with the estimating problem of response quantile with high dimensional covariates when response is missing at random. Some existing methods define root-n consistent estimators for the response quantile. But these methods require correct specifications of both the conditional distribution of response given covariates and the selection probability function. In this paper, a debiased method is proposed by solving a convex programming. The estimator obtained by the proposed method is asymptotically normal given a correctly specified parametric model for the condition distribution function, without the requirement to specify and estimate the selection probability function. Moreover, the proposed estimator is asymptotically more efficient than the existing estimators. The proposed method is evaluated by a simulation study and is illustrated by a real data example.