Bias prevention of maximum likelihood estimates for scalar skew normal and skew t distributions |
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| Institution: | 1. School of Finance and Statistics, East China Normal University, Shanghai 200241, China;2. H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA;1. Department of Statistics, Ankara University, 06100 Tandoğan, Ankara, Turkey;2. Turkish Statistical Institute, 06100, Ankara, Turkey;1. Centre for Trials Research, Cardiff University, Cardiff CF14 4YS, Wales, UK;2. School of Healthcare Sciences, Cardiff University, Cardiff CF14 4YS, Wales, UK;3. York Trials Unit, University of York, York, England, UK;4. Department of Health Sciences, University of York, York, England, UK;1. Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy;2. Zentrum Mathematik, Technische Universität München, Boltzmannstraße 3, 85748 Garching bei München, Germany |
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| Abstract: | The skew normal model is a class of distributions that extends the Gaussian family 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. As a solution, we use a modified score function as an estimating equation for the shape parameter. It is proved that the resulting modified maximum likelihood estimator is always finite. For confidence intervals a quasi-likelihood approach is considered. 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 known. |
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