Sample Quantile Estimation for Ignorable Nonresponse

Quantile estimation is widely used in clinical trials, social statistics and economics. In practise, complete data are often not available for every subject due to many reasons. In this article, we study the estimation of sample quantiles of response under missing at random assumption. We use noparametric kernel regression imputation method and local multiple imputation method to estimate sample quantiles. Asymptotic properties are also established and a revised bootstrap method is proposed to estimate the asymptotic variance of the two estimators. Simulation studies are reported to assess the finite sample properties of the proposed estimators. The merit of our methods are that, firstly, we don't need to give any assumptions on the missing response model; secondly, our method can deal with other non-differentiable estimation functions; finally, our method can be extended to solve other M estimator, and can estimate several quantiles simultaneously.