Imputation of missing values using quantile regression

Abstract

In this thesis, we consider an imputation method to handle missing response values based on quantile regression estimation. In the proposed method, the missing response values are generated using the estimated conditional quantile regression function at given values of covariates parametrically or semiparametrically. We adopt the generalized method of moments and the empirical likelihood method for estimation of parameters defined through a general estimating equation. We demonstrate that the proposed estimators, which combine both quantile regression imputation (parametric or semiparametric) and general estimating equation methods (generalized method of moments or empirical likelihood), have competitive advantages over some of the most widely used parametric and non-parametric imputation estimators. The consistency and the asymptotic normality of our estimators are established and variance estimation is provided. Results from a limited simulation study and an empirical study are presented to show the adequacy of the proposed methods.