Description:
The seminar will deal with some results about inference based on phi-divergence measures, under assumptions of Generalized Linear Models with binary data. The minimum phi-divergence estimator, which is seen to be a generalization of the maximum likelihood estimator is considered. This estimator is used in a phi-divergence measurement, which is basis of new statistics for solving some important problems regarding the Generalized Linear Models with binary data: fitting the model, residuals and dimensional reduction.
Some simulation studies are carried out in order to see the behavior of the minimum phi-divergence estimators and phi-divergence statistics considered in the talk. Finally, an extension of the previous results is presented, when a multinomal response is considered instead of a binary response.