Empirical Bayes One-side Test for Inverse Exponential Model based on Negative Associate Samples
American Journal of Theoretical and Applied Statistics
Volume 5, Issue 6, November 2016, Pages: 342-347
Received: Sep. 5, 2016;
Accepted: Sep. 23, 2016;
Published: Oct. 15, 2016
Views 3094 Downloads 98
Guobing Fan, Department of Basic Subjects, Hunan University of Finance and Economics, Changsha, China
By using the kernel-type density estimation and empirical distribution function in the case of identically distributed and negatively associated samples, the empirical Bayes one-sided test rules for the parameter of inverse exponential distribution are constructed based on negative associate sample under weighted linear loss function, and the asymptotically optimal property 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 One-side Test for Inverse Exponential Model based on Negative Associate Samples, American Journal of Theoretical and Applied Statistics.
Vol. 5, No. 6,
2016, pp. 342-347.
Robbins H., 1956. An empirical Bayes approach to statistics. Annals of Mathematical Statistics, 35(1): 1-20.
Karunamuni R. J., 1996. Empirical Bayes sequential estimation for exponential families: the untruncated component. Annals of the Institute of Statistical Mathematics, 48(4): 711-730.
Phipson B., Lee S., Majewski I. J. Alexander W. S., Smyth G. K., 2013. Empirical Bayes in the presence of exceptional cases, with application to microarray data. Phytochemistry, 26(8): 2247-2250.
Prakash G., 2015. Reliability performances based on empirical Bayes censored Gompertz data. International Journal of Advanced Research, 3(11):1297-1307.
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.
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.
Karunamuni, R. J. (1999). Optimal rates of convergence of monotone empirical Bayes tests for uniform distributions. Statistics & Decisions, 17(1), 63-86.
Xu, Y. S., Xu, Y., & Shi, Y. M. (2006). Convergence rates of empirical Bayes test for one-side truncation parameters with asymmetric loss functions. International Journal of Pure & Applied Mathematics, 27(1), 21-29.
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.
Shao Q. M., 2000. A comparison theorem on moment inequalities between negatively associated and independent random variables. Journal of Theoretical Probability, 13(2): 343-356.
Sung S. H., 2009. An exponential inequality for negatively associated random variables. Electronic Journal of Statistics, 3(1): 171-174.
Wei L., 2000. The empirical Bayes test problem for scale exponential family: in the case of NA samples. Acta Mathematicae Applicatae Sinica, 23(3: 403-412.
Shi Y., Shi X., Yan J., 2005. Two-sided empirical Bayes test for truncation parameter using NA samples. Information Sciences, 173(1-3): 65-74.
Wang L., Shi Y. M., 2008. The empirical Bayes test for one exponential family using NA samples. Journal of Northwest University, 38(4): 523-526.
Esary J. D.,1983. Negative association of random variables, with applications. Annals of Statistics, 11(1): 286-295.
Lin C., Duran B., Lewis T., 1989. Inverted Gamma as a life distribution. Microelectronics and Reliability, 29(4): 619-626.
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.