Empirical Bayes Test for Parameter of Inverse Exponential Distribution

Guobing Fan

doi:doi:10.11648/j.sjams.20160405.17

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Empirical Bayes Test for Parameter of Inverse Exponential Distribution

Guobing Fan

Published in Science Journal of Applied Mathematics and Statistics (Volume 4, Issue 5)

Received: 4 September 2016 Accepted: 12 September 2016 Published: 8 October 2016

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Abstract

The aim of this paper is to study the empirical Bayes test for the parameter of inverse exponential distribution. First, the Bayes test rule of one-sided test is derived in the case of independent and identically distributed random variables under weighted linear loss function. Then the empirical Bayes one-sided test rule is constructed by using the kernel-type density function and empirical distribution function. Finally, the asymptotically optimal property of the test function is obtained. It is shown that the convergence rates of the proposed empirical Bayes test rules can arbitrarily close to O(n^-1/2) under suitable conditions.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 4, Issue 5)
DOI	10.11648/j.sjams.20160405.17
Page(s)	236-241
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), 2016. Published by Science Publishing Group

Keywords

Empirical Bayes Test, Asymptotic Optimality, Convergence Rates, Weighted Linear Loss Function, Inverse Exponential Distribution

References

[1]	Petrone S., Rizzelli S., Rousseau J., Scricciolo C., 2014. Empirical Bayes methods in classical and Bayesian inference. Metron, 72 (2): 201-215.
[2]	Prakash G., 2015. Reliability performances based on empirical Bayes censored Gompertz data. International Journal of Advanced Research, 3 (11): 1297-1307.
[3]	Guarino C. M., Maxfield M., Reckase M. D., Thompson P. N., Wooldridge J. M., 2015. An evaluation of empirical bayes's estimation of value-added teacher performance measures. Journal of Educational & Behavioral Statistics, 40 (2): 190-222.
[4]	Coram M., Candille S., Duan, Q., Chan K. H., Li Y., Kooperberg C., et al., 2015. Leveraging multi-ethnic evidence for mapping complex traits in minority populations: an empirical Bayes approach. American Journal of Human Genetics, 96 (5): 740-52.
[5]	Spencer A. V., Cox A., Lin W. Y., Easton D. F., Michailidou K., Walters K., 2016. Incorporating functional genomic information in genetic association studies using an empirical Bayes approach. Genetic Epidemiology, 40 (3): 176-187.
[6]	Naznin F., Currie G., Sarvi M., Logan D., 2015. An empirical Bayes safety evaluation of tram/streetcar signal and lane priority measures in melbourne. Traffic Injury Prevention, 17 (1): 91-97.
[7]	Qian Z., Wei L., 2013. The two-sided empirical Bayes test of parameters for scale exponential family under weighed loss function. Journal of University of Science & Technology of China, 2 (2): 156-161.
[8]	Chen J., Jin Q., Chen Z., Liu C., 2013. Two-sided empirical Bayes test for the exponential family with contaminated data. Wuhan University Journal of Natural Sciences, 18 (6): 466-470.
[9]	Wang L., Shi Y. M., Chang P., 2012. Empirical Bayes test for two-parameter exponential distribution under Type-Ⅱ censored samples. Chinese Quarterly Journal of Mathematics, 27 (1): 54-58.
[10]	Lei Q., Qin Y., 2015. Empirical bayes test problem in continuous one-parameter exponential families under dependent samples. Sankhya Ser A, 77 (2): 364-379.
[11]	Ling C., Wei L., 2009. Convergence rates of the empirical Bayes test problem for continuous one-parameter exponential family. Journal of Systems Science & Mathematical Sciences, 29 (29): 1142-1152.
[12]	Guo P. J., Wang H. Y., Zhang T., 2009. The empirical Bayes test of the parameter for the scale-exponential family under PA samples [J]. Journal of Northwest University, 39(1): 1-5.
[13]	Liang W., Shi Y. M., 2010. Empirical bayes test for parameters of the linear exponential distribution with nqd random samples. Chinese Journal of Engineering Mathematics, 27 (4): 599-604.
[14]	Rao G. S., 2013. Estimation of reliability in multicomponent stress-strength based on inverse exponential distribution, International Journal of Statistics and Economics, 10 (1): 28-37.
[15]	Prakash G., 2012. Inverted exponential distribution under a Bayesian viewpoint. Journal of Modern Applied Statistical Methods, 11 (1): 190-202.
[16]	Singh S., Tripathi Y. M., Jun C. H., 2015. Sampling plans based on truncated life test for a generalized inverted exponential distribution. Industrial Engineering & Management Systems, 14 (2): 183-195.
[17]	Johns, M. V., 1972. Convergence rates for empirical Bayes two-action problems ii. continuous case. Annals of Mathematical Statistics, 43 (3): 934-947.
[18]	Chen J. Q, Liu C. H., 2008. Empirical Bayes test problem for the parameter of linear exponential distribution. Journal of Systems Science and Mathematical Sciences, 28 (5): 616-626.

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Guobing Fan. (2016). Empirical Bayes Test for Parameter of Inverse Exponential Distribution. Science Journal of Applied Mathematics and Statistics, 4(5), 236-241. https://doi.org/10.11648/j.sjams.20160405.17

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ACS Style

Guobing Fan. Empirical Bayes Test for Parameter of Inverse Exponential Distribution. Sci. J. Appl. Math. Stat. 2016, 4(5), 236-241. doi: 10.11648/j.sjams.20160405.17

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AMA Style

Guobing Fan. Empirical Bayes Test for Parameter of Inverse Exponential Distribution. Sci J Appl Math Stat. 2016;4(5):236-241. doi: 10.11648/j.sjams.20160405.17

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@article{10.11648/j.sjams.20160405.17,
  author = {Guobing Fan},
  title = {Empirical Bayes Test for Parameter of Inverse Exponential Distribution},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {4},
  number = {5},
  pages = {236-241},
  doi = {10.11648/j.sjams.20160405.17},
  url = {https://doi.org/10.11648/j.sjams.20160405.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20160405.17},
  abstract = {The aim of this paper is to study the empirical Bayes test for the parameter of inverse exponential distribution. First, the Bayes test rule of one-sided test is derived in the case of independent and identically distributed random variables under weighted linear loss function. Then the empirical Bayes one-sided test rule is constructed by using the kernel-type density function and empirical distribution function. Finally, the asymptotically optimal property of the test function is obtained. It is shown that the convergence rates of the proposed empirical Bayes test rules can arbitrarily close to O(n-1/2) under suitable conditions.},
 year = {2016}
}

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TY  - JOUR
T1  - Empirical Bayes Test for Parameter of Inverse Exponential Distribution
AU  - Guobing Fan
Y1  - 2016/10/08
PY  - 2016
N1  - https://doi.org/10.11648/j.sjams.20160405.17
DO  - 10.11648/j.sjams.20160405.17
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 236
EP  - 241
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20160405.17
AB  - The aim of this paper is to study the empirical Bayes test for the parameter of inverse exponential distribution. First, the Bayes test rule of one-sided test is derived in the case of independent and identically distributed random variables under weighted linear loss function. Then the empirical Bayes one-sided test rule is constructed by using the kernel-type density function and empirical distribution function. Finally, the asymptotically optimal property of the test function is obtained. It is shown that the convergence rates of the proposed empirical Bayes test rules can arbitrarily close to O(n-1/2) under suitable conditions.
VL  - 4
IS  - 5
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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Plain Text BibTeX RIS

APA Style

Guobing Fan. (2016). Empirical Bayes Test for Parameter of Inverse Exponential Distribution. Science Journal of Applied Mathematics and Statistics, 4(5), 236-241. https://doi.org/10.11648/j.sjams.20160405.17

Copy | Download

ACS Style

Guobing Fan. Empirical Bayes Test for Parameter of Inverse Exponential Distribution. Sci. J. Appl. Math. Stat. 2016, 4(5), 236-241. doi: 10.11648/j.sjams.20160405.17

Copy | Download

AMA Style

Guobing Fan. Empirical Bayes Test for Parameter of Inverse Exponential Distribution. Sci J Appl Math Stat. 2016;4(5):236-241. doi: 10.11648/j.sjams.20160405.17

Copy | Download

@article{10.11648/j.sjams.20160405.17,
  author = {Guobing Fan},
  title = {Empirical Bayes Test for Parameter of Inverse Exponential Distribution},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {4},
  number = {5},
  pages = {236-241},
  doi = {10.11648/j.sjams.20160405.17},
  url = {https://doi.org/10.11648/j.sjams.20160405.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20160405.17},
  abstract = {The aim of this paper is to study the empirical Bayes test for the parameter of inverse exponential distribution. First, the Bayes test rule of one-sided test is derived in the case of independent and identically distributed random variables under weighted linear loss function. Then the empirical Bayes one-sided test rule is constructed by using the kernel-type density function and empirical distribution function. Finally, the asymptotically optimal property of the test function is obtained. It is shown that the convergence rates of the proposed empirical Bayes test rules can arbitrarily close to O(n-1/2) under suitable conditions.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Empirical Bayes Test for Parameter of Inverse Exponential Distribution
AU  - Guobing Fan
Y1  - 2016/10/08
PY  - 2016
N1  - https://doi.org/10.11648/j.sjams.20160405.17
DO  - 10.11648/j.sjams.20160405.17
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 236
EP  - 241
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20160405.17
AB  - The aim of this paper is to study the empirical Bayes test for the parameter of inverse exponential distribution. First, the Bayes test rule of one-sided test is derived in the case of independent and identically distributed random variables under weighted linear loss function. Then the empirical Bayes one-sided test rule is constructed by using the kernel-type density function and empirical distribution function. Finally, the asymptotically optimal property of the test function is obtained. It is shown that the convergence rates of the proposed empirical Bayes test rules can arbitrarily close to O(n-1/2) under suitable conditions.
VL  - 4
IS  - 5
ER  -

Copy | Download