Marginal $M-$estimation under a general regression model with missing responses and covariates

BIANCO, ANA; BOENTE, GRACIELA; GONZALEZ-MANTEIGA, WENCESLAO; PEREZ-GONZALEZ, ANA

Leuven

Workshop; Workshop Celebrating Peter Rousseeuw's 60th Birthday; 2017

University of Leuven

In this talk, we will consider a general regression model where missingdata occur, both in the responses and in the covariates. Our aim is to discussthe estimation of any marginal functional, such as the median or an $M-$location functional of the response variable. A missing at randomcondition is assumed in order to prevent from bias in the estimation ofthe marginal measures under a non-ignorable missing mechanism. Differentapproaches for the estimation of the marginal functional of interest willbe presented, including inverse probability weighting, the convolution ofthe residual distribution and of the regression function and also an augmented inverse probability weighting, which protects against misspecification of theregression or the missing probability models. Consistency results are derived under a general framework. The small sample behaviour of the proposals will be illustrated through a Monte Carlo study.