Rank‐based inference with responses missing not at random

Abstract

Missing data have become almost inevitable whenever data are collected. In this paper, interest is given to responses missing not at random in the context of regression modeling. Many of the existing methods for estimating the model parameters lack robustness or efficiency. We propose a robust and efficient approach towards estimating the true regression parameters when some responses in the regression model are missing not at random. Large sample properties of the proposed estimator are established under mild regularity conditions. Monte Carlo simulation experiments are carried out and they showed that the proposed estimator is more efficient than the least squares estimator whenever the model error distribution is heavy tailed, contaminated or when data contain gross outliers. Finally, the method is illustrated using the ACTG protocol 315 data. The Canadian Journal of Statistics 46: 501–528; 2018 © 2018 Statistical Society of Canada