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.

Keywords:

• Fisher-consistency
• M-location functionals
• missing at random
• plug-in methods
• robust estimation

AMS Subject Classifications:

• MSC 62F35
• 62G08

Acknowledgments

The authors wish to thank the Associate Editor and two anonymous referees for valuable comments which led to an improved version of the original paper.

This work was partially developed while Ana M. Bianco and Graciela Boente were visiting the Departamento de Estatística, Análise Matemática e Optimización de la Universidad de Santiago de Compostela, Spain under the bilateral agreement between the Universidad de Buenos Aires and the Universidad de Santiago de Compostela. This research was partially supported by anpcyt under Grant pict 2018-00740 and Universidad de Buenos Aires under Grant 20020170100022BA, Argentina, and also by the Ministry of Economy and Competitiveness (MINECO/AEI/FEDER, UE) under the Spanish Project MTM2016-76969P, Spain. A. Bianco and G. Boente also wish to thank the Minerva Foundation for its support to present some of this paper results at the International Conference on Robust Statistics.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially developed while Ana M. Bianco and Graciela Boente were visiting the Departamento de Estatística, Análise Matemática e Optimización de la Universidad de Santiago de Compostela, Spain under the bilateral agreement between the Universidad de Buenos Aires and the Universidad de Santiago de Compostela. This research was partially supported by ANPCyT (grant number pict 2018-00740) and Universidad de Buenos Aires (grant number 20020170100022BA), Argentina, and also by the Ministry of Economy and Competitiveness (MINECO/AEI/FEDER, UE) under the Secretaría de Estado de Investigación, Desarrollo e Innovación Spanish Project MTM2016-76969P, Spain, which includes support from the European Regional Development Fund (ERDF).