Sartori, Nicola (2003) Bias prevention of maximum likelihood estimates: skew normal and skew t distributions. [Working Paper] WORKING PAPER SERIES, 1/2003 . , PADOVA
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The skew normal model is a class of distributions that extends the normal one by including a shape parameter. Despite its nice properties, this model presents some problems with the estimation of the shape parameter. In particular, for moderate sample sizes, the maximum likelihood estimator is infinite with positive probability. In this paper, we use the bias preventive method proposed by First (1993) to estimate the shape parameter. It is proved that this modified maximum likelihood estimator always exists finite. When regression and scale parameters are present, the method is combined with maximum likelihood estimators for these parameters. Finally, also the skew t distribution is considered, which may be viewed as an extension of the skew normal. The same method is applied to this model, considering the degrees of freedom as know.
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