Robust inference in generalized linear models with missing responses

BIANCO, ANA; BOENTE, GRACIELA; RODRIGUES, ISABEL

Londres

Conferencia; VIII International Conference of the ERCIM Working Group on Computing & Statistics (ERCIM2015).; 2015

Imperial College, Birkbeck University,Queen Mary University of London, Royal Statistical Society

When dealing with situations in which the responses are discrete or show some type of asymmetry, the linear model may be not appropriate to establish the relation between the responses and the covariates. Generalized linear models serve this purpose, since they allow one to model the mean of the responses through a link function linearly on the covariates. However, sometimes in practice response variables may be missing and some atypical observations may arise. To overcome this situation, we introduce robust procedures to estimate the regression parameter, under a generalized linear model, when missing data possibly occur in the responses. The robustness of the proposed procedures is studied through the influence function. Besides, outlier detection rules are defined using the influence function. Using that the robust estimators are asymptotically normally distributed we construct a robust Wald typeprocedure. A simulation study allows us to compare the behaviour of the classical and robust procedures, under different contamination schemes. Applications to real data set s enable to investigate the sensitivity of the Wald type test $p$ value to the missing scheme and to the presence of outliers.