Friday, October 19, 2007

A semiparametric framework for the generalized linear models: the logistic regression case

José António Santos

Abstract: The generalized linear models are an important family of parametric regression models. Inference based on these models depends on the specification assumptions and on severe regularity conditions. This is the general weakness of these models. It is presented here a semiparametric regression procedure based on a parametric formulation within the generalized linear models framework whose estimation is founded on the local maximum likelihood principle. This procedure could be applied virtually to any specification within the generalized linear models. A local maximum likelihood estimator based on logistic regression is presented as well as its bias, variance and asymptotic distribution. This semiparametric estimator is intended to be an alternative to the logistic regression that does not depend on severe regularity conditions and model specification accuracy. Some simulation results are presented. Two real data examples are also presented concerning HIV-infected men and mollusk imposex-affected females. This procedure is found to perform well and the results are encouraging. Future research arises from this work such as the bandwidth selection criteria and the optimal local polynomial degree for the bias estimator. The authors of this presentation have already extended this semiparametric procedure to count data regression analysis, namely to four local maximum likelihood estimators based on Poisson, negative binomial, ZIP and ZINB regression models.

Friday, October 19, 2007
Time: 11h30
Room: Sala Delta, Edificio Quelhas, ISEG