Liang, TaChen On an empirical Bayes test for a normal mean. (English) Zbl 1105.62301 Ann. Stat. 28, No. 2, 648-655 (2000). Summary: We exhibit an empirical Bayes test \(\delta_n^*\) for the normal mean testing problem using a linear error loss. Under the condition that the critical point of a Bayes test is within some known compact interval, \(\delta_n^*\) is shown to be asymptotically optimal and its associated regret Bayes risk converges to zero at a rate \(O(n^{-1}(\ln n)^{1.5})\), where n is the number of past experiences available when the current component decision problem is considered. Under the same condition this rate is faster than the optimal rate of convergence claimed by Karunamuni. Cited in 2 ReviewsCited in 7 Documents MSC: 62C12 Empirical decision procedures; empirical Bayes procedures 62F03 Parametric hypothesis testing Keywords:Asymptotically optimal; empirical Bayes; rate of convergence × Cite Format Result Cite Review PDF Full Text: DOI Euclid References: [1] Fan, Jianqing (1991). On the optimal rates of convergence for nonparametric deconvolution problems. Ann. Statist. 19 1257-1272. · Zbl 0729.62033 · doi:10.1214/aos/1176348248 [2] Johns, M.V., Jr. and Van Ryzin, J. R. (1972). Convergence rates for empirical Bayes two-action problems, II. Continuous case. Ann. Math. Statist. 43 934-947. · Zbl 0249.62014 · doi:10.1214/aoms/1177692557 [3] Karunamuni, Rohana J. (1996). Optimal rates of convergence of empirical Bayes tests for the continuous one-parameter exponential family. Ann. Statist. 24 212-231. · Zbl 0853.62011 · doi:10.1214/aos/1033066207 [4] Pensky, M. (1997). Empirical Bayes estimation of location-parameter. Statist. Decisions 15 1-16. · Zbl 0883.62006 [5] Robbins, H. (1956). An empirical Bayes approach to statistics. Proc. Third Berkeley Symp. Math. Statist. Probab. 1 157-163. Univ. California Press, Berkeley. · Zbl 0074.35302 [6] Robbins, H. (1964). The empirical Bayes approach to statistical decision problems. Ann. Math. Statist. 35 1-20. · Zbl 0138.12304 · doi:10.1214/aoms/1177703729 [7] Van Houwelingen, J. C. (1976). Monotone empirical Bayes tests for the continuous one-parameter exponential family. Ann. Statist. 4 981-989. · Zbl 0339.62002 · doi:10.1214/aos/1176343596 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.