# Weighted empirical likelihood for quantile regression with nonignorable missing covariates

## TL;DR

This paper introduces a weighted empirical likelihood estimator for quantile regression that effectively handles nonignorable missing covariates, achieving efficiency gains over traditional methods.

## Contribution

It proposes a novel, computationally simple estimator that attains semiparametric efficiency under correct missingness probability specification.

## Key findings

- The estimator is computationally simple.
- It achieves semiparametric efficiency.
- Simulation and real data demonstrate improved performance.

## Abstract

In this paper, we propose an empirical likelihood-based weighted estimator of regression parameter in quantile regression model with nonignorable missing covariates. The proposed estimator is computationally simple and achieves semiparametric efficiency if the probability of missingness on the fully observed variables is correctly specified. The efficiency gain of the proposed estimator over the complete-case-analysis estimator is quantified theoretically and illustrated via simulation and a real data application.