On non-existence of moment estimators of the GED power parameter

Bartosz Stawiarski

Discussiones Mathematicae Probability and Statistics (2016)

  • Volume: 36, Issue: 1-2, page 5-23
  • ISSN: 1509-9423

Abstract

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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.

How to cite

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Bartosz Stawiarski. "On non-existence of moment estimators of the GED power parameter." Discussiones Mathematicae Probability and Statistics 36.1-2 (2016): 5-23. <http://eudml.org/doc/286900>.

@article{BartoszStawiarski2016,
abstract = {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.},
author = {Bartosz Stawiarski},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {Generalized Error Distribution; nonparametric bootstrap; bootstrap consistency; moment estimator; power parameter},
language = {eng},
number = {1-2},
pages = {5-23},
title = {On non-existence of moment estimators of the GED power parameter},
url = {http://eudml.org/doc/286900},
volume = {36},
year = {2016},
}

TY - JOUR
AU - Bartosz Stawiarski
TI - On non-existence of moment estimators of the GED power parameter
JO - Discussiones Mathematicae Probability and Statistics
PY - 2016
VL - 36
IS - 1-2
SP - 5
EP - 23
AB - 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.
LA - eng
KW - Generalized Error Distribution; nonparametric bootstrap; bootstrap consistency; moment estimator; power parameter
UR - http://eudml.org/doc/286900
ER -

References

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