Robust Approach for the Location Estimation in a Missing Data Setting.

SUED, M.; YOHAI, V. J.

Praga

Congreso; International Conference on Robust Statistics.; 2010

ICORS

In a missing-data setting, we have a sample in which a vector ofexplanatory variables xi is observed for every subjecti, while scalar outcomes yi are missing by happenstance onsome individuals. In this work we propose robust estimates of thedistribution of the responses assuming missing at random (MAR) data,under a semiparametric regression model. Our approach allows theconsistent estimation of any weakly continuous functional of theresponse´s distribution. In particular, strongly consistentestimates of any continuous location functional, such as the medianor MM functionals, are proposed. A robust fit for the regressionmodel combined with the robust properties of the location functionalgives rise to a robust recipe for estimating the location parameter.Robustness is quantified through the breakdown point of the proposedprocedure. The asymptotic distribution of the location estimates isalso derived.