We study empirical Bayes estimation of the guarantee lifetime θ in a two-parameter exponential distribution having a probability density p(x|θ,β)=(1/β)exp(-(x-θ)/β)I(x-θ) with unknown scale parameter β. An empirical Bayes estimator is proposed and its associated asymptotic optimality is studied. It is shown that is asymptotically optimal in the sense that its regret converges to zero at a rate n-2r/(2r+1), where n is the number of past observations available and r is a positive integer related to the prior distribution G.
Relation:
Statistics and Probability Letters 76(16), pp.1821-1829
