Skewness of maximum likelihood estimators in dispersion models |
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| Authors: | Alexandre B Simas Gauss M Cordeiro Andréa V Rocha |
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| Institution: | 1. Associação Instituto Nacional de Matemática Pura e Aplicada, IMPA, Estrada D. Castorina, 110, Jd. Botânico, 22460-320 Rio de Janeiro-RJ, Brazil;2. Departamento de Estatística e Informática, Universidade Federal Rural de Pernambuco, Rua Dom Manoel de Medeiros s/n, Dois Irmãos, 52171-900 Recife-PE, Brazil;3. Departamento de Estatística, Universidade Federal da Paraíba, Cidade Universitária - Campus I, 58051-970 João Pessoa-PB, Brazil |
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| Abstract: | We introduce the dispersion models with a regression structure to extend the generalized linear models, the exponential family nonlinear models (Cordeiro and Paula, 1989) and the proper dispersion models (Jørgensen, 1997a). We provide a matrix expression for the skewness of the maximum likelihood estimators of the regression parameters in dispersion models. The formula is suitable for computer implementation and can be applied for several important submodels discussed in the literature. Expressions for the skewness of the maximum likelihood estimators of the precision and dispersion parameters are also derived. In particular, our results extend previous formulas obtained by Cordeiro and Cordeiro (2001) and Cavalcanti et al. (2009). A simulation study is performed to show the practice importance of our results. |
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| Keywords: | Dispersion models Nonlinear models Skewness Maximum likelihood |
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