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.

翻译：本文关注随机缺少响应时反应量与高维共变的响应量的估计问题。 有些现有方法定义了响应量的根- 一致估计值。 但是这些方法需要附带共变数的有条件响应分布和选择概率功能的正确规格。 在本文中, 通过解析一个 convex 编程, 提出一个偏差的方法。 使用拟议方法获得的估计值是平庸的, 给条件分布功能一个正确指定的参数模型, 不需要指定和估计选择概率函数。 此外, 拟议的估计值比现有的估计值要简单有效。 提议的方法通过模拟研究得到评估, 并用真实的数据示例加以说明 。