Asymptotic Optimal Empirical Bayes Estimation of the Parameter of ЭРланга Distribution

Guobing Fan

doi:doi:10.11648/j.ajam.20160406.14

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Asymptotic Optimal Empirical Bayes Estimation of the Parameter of ЭРланга Distribution

Guobing Fan

Published in American Journal of Applied Mathematics (Volume 4, Issue 6)

Received: 6 October 2016 Accepted: 14 October 2016 Published: 7 November 2016

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Abstract

This paper aims to study the empirical Bayes estimation of the parameter of ЭРланга distribution under a weighted squared error loss function. Bayes estimator is firstly to derive based on pivot method. Then empirical Bayes estimator of unknown parameter is constructed in a priori unknown circumstances. The asymptotically optimal property of this empirical Bayes estimator is also discussed. It is shown that the convergence rates of the proposed empirical Bayes estimator can arbitrarily close to O(n) ^-1) under suitable conditions.

Published in	American Journal of Applied Mathematics (Volume 4, Issue 6)
DOI	10.11648/j.ajam.20160406.14
Page(s)	283-288
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Empirical Bayes Estimator, Asymptotic Optimality, Weighted Squared Error Loss Function, ЭРланга Distribution

References

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APA Style

Guobing Fan. (2016). Asymptotic Optimal Empirical Bayes Estimation of the Parameter of ЭРланга Distribution. American Journal of Applied Mathematics, 4(6), 283-288. https://doi.org/10.11648/j.ajam.20160406.14

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ACS Style

Guobing Fan. Asymptotic Optimal Empirical Bayes Estimation of the Parameter of ЭРланга Distribution. Am. J. Appl. Math. 2016, 4(6), 283-288. doi: 10.11648/j.ajam.20160406.14

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AMA Style

Guobing Fan. Asymptotic Optimal Empirical Bayes Estimation of the Parameter of ЭРланга Distribution. Am J Appl Math. 2016;4(6):283-288. doi: 10.11648/j.ajam.20160406.14

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@article{10.11648/j.ajam.20160406.14,
  author = {Guobing Fan},
  title = {Asymptotic Optimal Empirical Bayes Estimation of the Parameter of ЭРланга Distribution},
  journal = {American Journal of Applied Mathematics},
  volume = {4},
  number = {6},
  pages = {283-288},
  doi = {10.11648/j.ajam.20160406.14},
  url = {https://doi.org/10.11648/j.ajam.20160406.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160406.14},
  abstract = {This paper aims to study the empirical Bayes estimation of the parameter of ЭРланга distribution under a weighted squared error loss function. Bayes estimator is firstly to derive based on pivot method. Then empirical Bayes estimator of unknown parameter is constructed in a priori unknown circumstances. The asymptotically optimal property of this empirical Bayes estimator is also discussed. It is shown that the convergence rates of the proposed empirical Bayes estimator can arbitrarily close to O(n) -1) under suitable conditions.},
 year = {2016}
}

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TY  - JOUR
T1  - Asymptotic Optimal Empirical Bayes Estimation of the Parameter of ЭРланга Distribution
AU  - Guobing Fan
Y1  - 2016/11/07
PY  - 2016
N1  - https://doi.org/10.11648/j.ajam.20160406.14
DO  - 10.11648/j.ajam.20160406.14
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 283
EP  - 288
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20160406.14
AB  - This paper aims to study the empirical Bayes estimation of the parameter of ЭРланга distribution under a weighted squared error loss function. Bayes estimator is firstly to derive based on pivot method. Then empirical Bayes estimator of unknown parameter is constructed in a priori unknown circumstances. The asymptotically optimal property of this empirical Bayes estimator is also discussed. It is shown that the convergence rates of the proposed empirical Bayes estimator can arbitrarily close to O(n) -1) under suitable conditions.
VL  - 4
IS  - 6
ER  -

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Author Information

Guobing Fan

Department of Basic Subjects, Hunan University of Finance and Economics, Changsha, China

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APA Style

Guobing Fan. (2016). Asymptotic Optimal Empirical Bayes Estimation of the Parameter of ЭРланга Distribution. American Journal of Applied Mathematics, 4(6), 283-288. https://doi.org/10.11648/j.ajam.20160406.14

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ACS Style

Guobing Fan. Asymptotic Optimal Empirical Bayes Estimation of the Parameter of ЭРланга Distribution. Am. J. Appl. Math. 2016, 4(6), 283-288. doi: 10.11648/j.ajam.20160406.14

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AMA Style

Guobing Fan. Asymptotic Optimal Empirical Bayes Estimation of the Parameter of ЭРланга Distribution. Am J Appl Math. 2016;4(6):283-288. doi: 10.11648/j.ajam.20160406.14

Copy | Download

@article{10.11648/j.ajam.20160406.14,
  author = {Guobing Fan},
  title = {Asymptotic Optimal Empirical Bayes Estimation of the Parameter of ЭРланга Distribution},
  journal = {American Journal of Applied Mathematics},
  volume = {4},
  number = {6},
  pages = {283-288},
  doi = {10.11648/j.ajam.20160406.14},
  url = {https://doi.org/10.11648/j.ajam.20160406.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20160406.14},
  abstract = {This paper aims to study the empirical Bayes estimation of the parameter of ЭРланга distribution under a weighted squared error loss function. Bayes estimator is firstly to derive based on pivot method. Then empirical Bayes estimator of unknown parameter is constructed in a priori unknown circumstances. The asymptotically optimal property of this empirical Bayes estimator is also discussed. It is shown that the convergence rates of the proposed empirical Bayes estimator can arbitrarily close to O(n) -1) under suitable conditions.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Asymptotic Optimal Empirical Bayes Estimation of the Parameter of ЭРланга Distribution
AU  - Guobing Fan
Y1  - 2016/11/07
PY  - 2016
N1  - https://doi.org/10.11648/j.ajam.20160406.14
DO  - 10.11648/j.ajam.20160406.14
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 283
EP  - 288
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20160406.14
AB  - This paper aims to study the empirical Bayes estimation of the parameter of ЭРланга distribution under a weighted squared error loss function. Bayes estimator is firstly to derive based on pivot method. Then empirical Bayes estimator of unknown parameter is constructed in a priori unknown circumstances. The asymptotically optimal property of this empirical Bayes estimator is also discussed. It is shown that the convergence rates of the proposed empirical Bayes estimator can arbitrarily close to O(n) -1) under suitable conditions.
VL  - 4
IS  - 6
ER  -

Copy | Download