Resumen
This paper deals with the empirical Bayes testing for the mean ? of a N(?,s2) distribution using a linear error loss where it is assumed that ? follows an unknown prior distribution G and variance s2 is fixed but unknown. An empirical Bayes test d˜n is constructed. Under very mild conditions that EG[|?|]<8 and the critical point of a Bayes test is finite, d˜n is shown to be asymptotically optimal, and the associated regret converges to zero at a rate O(n-1(lnn)1.5)where n is the number of past experiences available when the current component decision problem is considered. This rate achieves the optimal rate which was established by Gupta and Li (Optimal rate of convergence of monotone empirical Bayes tests for a normal mean. Technical Report 01-03, Department of Statistics, Purdue University.) for variance s2 known case.

Resumen
In this paper, we study the problem of simultaneously inspecting n finite normal populations for variable equivalence with respect to a control. Our goal is to select all equivalent populations and to exclude all nonequivalences. By incorporating information from the samples taken from each of the n populations, an empirical Bayes simultaneous inspection procedure d~* is constructed. The relative regret of d~* is used as a measure of performance of d~*. It is proved that d~* is asymptotically optimal in the sense that the relative regret of d~* converges to zero at a rate n-1((lnn)(lnlnn))2.5.