During the 20th Century, statisticians have become acutely aware that common statistical procedures are very sensitive even to slight deviations from the assumed model. In regression analysis, the use of the least square method would not be appropriate in solving the problem of containing outliers or extreme observations. So, we need a parameter estimation method which is robust, where the value of the estimation is not much affected by small changes in the data. In this thesis, we introduced a resistant procedure to test hypothesis on the regression parameters under a generalized linear regression model, in which the mean of the responses is modelled through a link function linearly on the covariates , when there are missing observations in the responses and it can be suspected that anomalous observations are present in the sample. Although there are many situations in which both the response and the explanatory variables are missing, in this study we will focus on those cases in which missing data occur only in the responses. In practice, some response variables may be missing by design, as in two-stage studies, or by happenstance. Actually, missingness of responses is very common in opinion polls, market research surveys, mail enquiries, social-economic investigations, medical studies and other scientific experiments, when the explanatory variables can be controlled. Robust estimators for the regression parameters, in order to build test statistics for these parameters, when missing data occure in the responses , are considered. These estimators are natural extensions of the MM-estimators for linear models with asymmetric errors and have an indicator for missing responses and a weight function for control leverage points, which will be effective when testing hypothesis on the regression parameters. The asymptotic behavior of the robust estimators for the regression parameters is obtained, under the null hypothesis and under contiguous alternatives. This allows us to derive the asymptotic distribution of the robust Wald-type test statistics constructed from the proposed estimators. The influence function of the test statistics is also studied. A simulation study based on log-gamma model allows us to compare the behavior of the justify; MARGIN: 0cm 0cm 0pt" Finally through real data sets, we confirm the stability of the decision rule by tests based on proposed estimators, which are based on weights that control high leverage points, when outlying observations are present and under different missing probability patterns.