On empirical Bayes testing for a location parameter in a shifted gamma distribution

Consider a location parameter 0 in a. shifted gamma distribution having pdff(x/theta)=(x-theta)(alpha-1)exp{-(x-theta)}/Gamma(alpha)I-(theta,I- infinity)(x), where alpha greater than or equal to 2 is the fixed shape parameter. We study the two-action problem of testing H-0: theta < theta(0) against H-1 : theta > theta(0) using the empirical Bayes approach. An empirical Bayes test delta(n)* is constructed. Under some mild conditions, delta(n)(*) is shown to be asymptotically optimal at a rate of order O(n(-2(alpha-1)/(2alpha-1))) for alphagreater than or equal to2, where n is the number of past data available when the current decision problem is considered. The achieved rate of delta(n)* much improves the existing result in the literature.