Skewness of maximum likelihood estimators in dispersion models

Details Skewness of maximum likelihood estimators in dispersion models Skewness of maximum likelihood estimators in dispersion models

2010-01-13

arxiv.org/abs/1001.2187v1

Journal of Statistical Planning and Inference, 140, 2111-2121, 2010.

Statistics

Methodology

Scientific paper

10.1016/j.jspi.2010.02.007

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 (J{\o}rgensen, 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 perfomed to show the practice importance of our results.

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