Empirical likelihood for estimating equations with missing values

TL;DR

This paper introduces an empirical likelihood approach combined with nonparametric imputation to efficiently estimate parameters defined by general estimating equations in the presence of missing data, reducing bias and improving accuracy.

Contribution

It proposes a novel combination of empirical likelihood with kernel-based nonparametric imputation for handling missing data in estimating equations, enhancing estimation efficiency.

Findings

Imputation reduces selection bias in missing data scenarios.

Empirical likelihood improves parameter estimation accuracy.

Method performs well in simulations and real genetic data analysis.

Abstract

We consider an empirical likelihood inference for parameters defined by general estimating equations when some components of the random observations are subject to missingness. As the nature of the estimating equations is wide-ranging, we propose a nonparametric imputation of the missing values from a kernel estimator of the conditional distribution of the missing variable given the always observable variable. The empirical likelihood is used to construct a profile likelihood for the parameter of interest. We demonstrate that the proposed nonparametric imputation can remove the selection bias in the missingness and the empirical likelihood leads to more efficient parameter estimation. The proposed method is further evaluated by simulation and an empirical study on a genetic dataset on recombinant inbred mice.