Geodesic
On non-existence of moment estimators of the GED power parameter
Discussiones Mathematicae. Probability and Statistics, Tome 36 (2016) no. 1-2, pp. 5-23

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We reconsider the problem of the power (also called shape) parameter estimation within symmetric, zero-mean, unit-variance one-parameter Generalized Error Distribution family. Focusing on moment estimators for the parameter in question, through extensive Monte Carlo simulations we analyze the probability of non-existence of moment estimators for small and moderate samples, depending on the shape parameter value and the sample size. We consider a nonparametric bootstrap approach and prove its consistency. However, despite its established asymptotics, bootstrap does not substantially improve the statistical inference based on moment estimators once they fall into the non-existence area in case of small and moderate sample sizes.
Keywords: Generalized Error Distribution, nonparametric bootstrap, bootstrap consistency, moment estimator, power parameter 
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Stawiarski, Bartosz. On non-existence of moment estimators of the GED power parameter. Discussiones Mathematicae. Probability and Statistics, Tome 36 (2016) no. 1-2, pp. 5-23. http://geodesic.mathdoc.fr/item/DMPS_2016_36_1-2_a0/