Local influence in compound-poisson models: perturbing the mean-variance relation

Local influence is a useful tool to detect abnormalities in regression models, Cook proposed this method in 1986 for classical regression models and, since then, numerous extensions have been developed. The aim of this paper is to derive methods to asses local influence under various perturbation schemes, for compound-Poisson regression models. These models can be applied to continuous data with positive probability in zero, and they are characterized by the variance function that defines the mean-variance relationship. Formulas are obtained to apply local influence methods for different perturbations and it is of particular interest the perturbation of the parameter that defines the mean-variance relation. These schemes are applied to perturbed data generated by simulations and the sensibility of the method is compared for different values of the parameters. Finally, a real data set about home expenditures is analyzed and local influence graphics are obtained to detect influential points.