Science Journal of Applied Mathematics and Statistics
Volume 4, Issue 5, October 2016, Pages: 236-241
Received: Sep. 4, 2016;
Accepted: Sep. 12, 2016;
Published: Oct. 8, 2016
Views 2975 Downloads 94
Guobing Fan, Department of Basic Subjects, Hunan University of Finance and Economics, Changsha, China
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.
Empirical Bayes Test for Parameter of Inverse Exponential Distribution, Science Journal of Applied Mathematics and Statistics.
Vol. 4, No. 5,
2016, pp. 236-241.
Petrone S., Rizzelli S., Rousseau J., Scricciolo C., 2014. Empirical Bayes methods in classical and Bayesian inference. Metron, 72 (2): 201-215.
Prakash G., 2015. Reliability performances based on empirical Bayes censored Gompertz data. International Journal of Advanced Research, 3 (11): 1297-1307.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Prakash G., 2012. Inverted exponential distribution under a Bayesian viewpoint. Journal of Modern Applied Statistical Methods, 11 (1): 190-202.
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.
Johns, M. V., 1972. Convergence rates for empirical Bayes two-action problems ii. continuous case. Annals of Mathematical Statistics, 43 (3): 934-947.
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.