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B0348
Title: Minimum distance estimators for count data based on the probability generating function with applications Authors:  Maria Dolores Jimenez-Gamero - Universidad de Sevilla (Spain)
Apostolos Batsidis - University of Ioannina (Greece) [presenting]
Francisco Novoa-Munoz - Universidad del Bio-Bio (Chile)
Abstract: Parameter estimation is a crucial aspect of statistical data analysis. Maximum likelihood (ML) estimation is the most popular method of estimating the unknown parameters of a model. Although efficient, it is well-known that ML estimates are rather sensitive to outlying observations or/and computationally difficult if the corresponding probability density function or probability mass function is complicated. For these reasons, alternative procedures have been proposed and in this frame the use of transforms such as the characteristic function, the moment and the probability generating function in point estimation has been investigated. Specifically, when dealing with count data, inferential methods based on the empirical probability generating function have been proposed. Properties of parameter estimators obtained my minimizing a distance between the empirical probability generating function and the probability generating function of a model for count data are studied. Specifically, it is proved that, under certain not restrictive conditions, the resulting estimators are consistent and, suitably normalized, asymptotically normal, even if the model is misspecified. Applications of the obtained results to the goodness-of-fit problem, model selection problem and to the problem of testing for separate families of distributions are considered.