Rank-based estimating equation with non-ignorable missing responses via empirical likelihood

Abstract

In this paper, a general regression model with responses missing not at random is considered. From a rankbased estimating equation, a rank-based estimator of the regression parameter is derived. Based on this estimator's asymptotic normality property, a consistent sandwich estimator of its corresponding asymptotic covariance matrix is obtained. In order to overcome the over-coverage issue of the normal approximation procedure, the empirical likelihood based on the rank-based gradient function is defined, and its asymptotic distribution is established. Extensive simulation experiments under different settings of error distributions with different response probabilities are considered, and the simulation results show that the proposed empirical likelihood approach has better performance in terms of coverage probability and average length of confidence intervals for the regression parameters compared with the normal approximation approach and its least-squares counterpart. A real data example is provided to illustrate the proposed methods.

Sampling Importance Resampling Algorithm with Nonignorable Missing Response Variable Based on Smoothed Quantile Regression

“…Regarding nonrandom missing data, previous studies have addressed the issue in different regression settings. Specifically, Niu et al [13] and Bindele and Zhao [14] focused on estimation equation imputation in linear regression and rank regression, respectively. In the context of quantile regression, Chen et al [15] introduced three missing quantile regression estimation equations: inverse probability weighting, estimation equation imputation, and an enhanced approach combining both methods.…”