Generalized Method of Moments Estimator Based On Semiparametric Quantile Regression Imputation

TL;DR

This paper introduces a novel imputation method combining semiparametric quantile regression with the generalized method of moments to handle missing data, demonstrating theoretical properties and practical effectiveness.

Contribution

It proposes a new estimator integrating semiparametric quantile regression imputation with GMM, showing improved performance over existing methods.

Findings

Estimator is consistent and asymptotically normal.

Method performs well in simulations and empirical data.

Provides variance estimation for the proposed estimator.

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 estimated conditional quantile regression function at given values of covariates. We adopt the generalized method of moments for estimation of parameters defined through a general estimation equation. We demonstrate that the proposed estimator, which combines both semiparametric quantile regression imputation and generalized method of moments, has competitive edge against some of the most widely used parametric and non-parametric imputation estimators. The consistency and the asymptotic normality of our estimator 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 method.