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http://dx.doi.org/10.5351/CKSS.2008.15.2.213

Empirical Bayes Test for the Exponential Parameter with Censored Data  

Wang, Lichun (Department of Mathematics, Beijing Jiaotong University)
Publication Information
Communications for Statistical Applications and Methods / v.15, no.2, 2008 , pp. 213-228 More about this Journal
Abstract
Using a linear loss function, this paper considers the one-sided testing problem for the exponential distribution via the empirical Bayes(EB) approach. Based on right censored data, we propose an EB test for the exponential parameter and obtain its convergence rate and asymptotic optimality, firstly, under the condition that the censoring distribution is known and secondly, that it is unknown.
Keywords
Asymptotic optimality; convergence rate; empirical Bayes; random censorship;
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1 Johns, M. V. Jr. and Van Ryzin, J. R. (1972). Convergence rates for empirical Bayes two-action problem II: Continuous case. The Annals of Mathematical Statistics, 43, 934-947   DOI
2 Major, P. and Rejto, L. (1988). Strong embedding of the estimator of the distribution function under random censorship. The Annals of Statistics, 16, 1113-1132   DOI
3 Singh, R. S. (1979). Empirical Bayes estimation in lebesgue-exponential families with rates near the best possible rate. The Annals of Statistics, 7, 890-902   DOI
4 Robbins, H. (1964). The empirical Bayes approach to statistical decision problem. The Annals of Mathematical Statistics, 35, 1-20   DOI
5 Stijnen, T. (1985). On the asymptotic behaviour of empirical Bayes tests for the continuous one-parameter exponential family. The Annals of Statistics, 13, 403-412   DOI
6 Liang, T. C. (2000b). On an empirical Bayes test for a normal mean. The Annals of Statistics, 28, 648-655   DOI
7 Robbins, H. (1956). An empirical Bayes approach to statistics. In Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, 1, 157-163
8 Kaplan, E. L. and Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53, 457-481   DOI
9 Lemdani, M. and Ould-Sald, E. (2002). Exact asymptotic $L_1-error$ of a kernel density estimator under censored data. Statistics & Probability Letters, 60, 59-68   DOI   ScienceOn
10 Liang, T. C. (2000a). On empirical Bayes tests in a positive exponential family. Journal of Statistical Planning and Inference, 83, 169-181   DOI   ScienceOn
11 Karunamuni, R. J. and Yang, H. (1995). On convergence rates of monotone empirical Bayes tests for the continuous one-parameter exponential family. Statistics & Decisions, 13, 181-192
12 Foldes, A. and Rejto, L. (1981). Strong uniform consistency for nonparametric survival curve estimators from randomly censored data. The Annals Statistics, 19, 122-129
13 Van Houwelingen, J. C. (1976). Monotone empirical Bayes test for the continuous one-parameter exponential family. The Annals of Statistics, 4, 981-989   DOI
14 Singh, R. S. (1977). Applications of estimators of a density and its derivatives to certian statistical problems. Journal of the Royal Statistical Society, Ser. B, 39, 357-363
15 Johns, M. V. Jr. and Van Ryzin, J. R. (1971). Convergence rates for empirical Bayes two-action problem I: Discrete case. The Annals of Mathematical Statistics, 42, 1521-1539   DOI