  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.
