Robust methods in semiparametric estimation with missing responses

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

Colmenarejo

Workshop; International Workshop on Applied Probability (IWAP 2010); 2010

Most of the statistical methods in nonparametric regression are designed for complete data sets and problemsarise when missing observations are present which is a common situation in biomedical or socioeconomic studies,for example. Classic examples are found in the field of social sciences with the problem of non-response in samplesurveys, in Physics, in Genetics, among others. We will consider inference with an incomplete data set wherethe responses satisfy a semiparametric partly linear regression model and we will introduce a family of robustprocedures to estimate the regression parameter as well as the marginal location of the responses, when thereare missing observations in the response variable, but the covariates are totally observed. In this context, it isnecessary to require some conditions regarding the loss of an observation. We model the aforementioned lossassuming that the data are missing at random, i.e, the probability of observing a missing data is independent ofthe response variable, and it only depends on the covariate. Our proposal is based on a robust profile likelihoodapproach adapted to the presence of missing data. We derive the asymptotic behavior of the robust estimatorsfor the regression parameter and of a weighted simplified location estimator. For the latter, the asymptoticdistribution is derived when the missing probability is known and also when it is estimated. A Monte Carlo studyis carried out to compare the performance of the robust proposed estimators among them and also with theclassical ones, in normal and contaminated samples, under different missing data models.