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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1185,
author = {Bartosz Stawiarski},
title = {On non-existence of moment estimators of the GED power parameter},
journal = {Discussiones Mathematicae Probability and Statistics},
volume = {36},
year = {2016},
pages = {5-23},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1185}
}
Bartosz Stawiarski. On non-existence of moment estimators of the GED power parameter. Discussiones Mathematicae Probability and Statistics, Tome 36 (2016) pp. 5-23. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1185/
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