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), 2024. Published by Science Publishing Group |
Empirical Bayes Test, Asymptotic Optimality, Convergence Rates, Weighted Linear Loss Function, Inverse Exponential Distribution
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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
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
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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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}
}
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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