Parameter estimation through semiparametric quantile regression imputation

Abstract

In this article, we consider an imputation method to handle missing response values based on semiparametric quantile regression estimation. In the proposed method, the missing response values are generated using the semiparametrically estimated conditional quantile regression function at given values of covariates. Then the imputed values are used to estimate a parameter defined as the expected value of a function involving the response and covariate variables. We derive the asymptotic distribution of our estimator constructed with the imputed data and provide a variance estimator. In simulation, we compare our semiparametric quantile regression imputation method to fully parametric and nonparametric alternatives and evaluate the variance estimator based on the asymptotic distribution. We also discuss an extension for estimating a parameter defined through an estimation equation.