Robust location estimators in regression models with covariates and responses missing at random

Abstract

This paper deals with robust marginal estimation under a general regression model when missing data occur in the response and also in some covariates. The target is a marginal location parameter given through an M-functional. To obtain robust Fisher-consistent estimators, properly defined marginal distribution function estimators are considered. These estimators avoid the bias due to missing values assuming a missing at random condition. Three methods are considered to estimate the marginal distribution which allows to obtain the M-location of interest: the well-known inverse probability weighting, a convolution-based method that makes use of the regression model and an augmented inverse probability weighting procedure that prevents against misspecification. Different aspects of their asymptotic behaviour are derived under regularity conditions. The robust studied estimators and their classical relatives are compared through numerical experiments under different missing data models, including clean and contaminated samples. The methodology is illustrated through a real data set.