Generalized Linear Models with Missing Response: a Robust Approach

BIANCO, ANA; BOENTE, GRACIELA; RODRIGUES, ISABEL

Buenos Aires

Encuentro; Octavo Encuentro Regional de Probabilidad y Estadistica Matematica (8vo. ERPEM; 2011

Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Universidad de San Andrés y Universidad Torcuato Di Tella

When dealing with situations in which the responses are discrete or show some type of asymmetry,the linear model is not appropriate to establish the relation between the responses and the covariates. Generalized linear models (glm) serve this purpose, since they allow to model the mean of the responses through a link function, linearly on the covariates. When atypical observations are present in the sample, robust estimators are useful to provide fair estimations and also to build outlier detection rules. We focus on robust inference procedures involving the regression parameter of a glm when missing data possibly occur in the responses. First, we propose robust general M-estimators. We study the asymptotic behaviour of the proposed estimators: they turn out to be consistent under mild assumptions and asymptotically normal, as well. Besides, outlier detection rules are defined using the influence function. Secondly, robust Wald type tests are derived. The Poisson and Gamma regression models are considered as special cases. By means of a simulation study we compare the behaviour of the classical and robust procedures, under different contamination and missing probability schemes. We also illustrate the usefulness of the proposals through some real data sets.