Abstract: Under the weighed loss function, the two-sided empirical Bayes (EB) test of parameters for the scale exponential family was discussed. The EB test rules were constructed by kernel estimation method. The asymptotical optimality and convergence rates of the EB test rules were obtained. Finally, an example satisfying the conditions of the theorem was shown.

Key words: scale exponential family, two-sided empirical Bayes test, weighed product loss function, asymptotically optimality, convergence rate