Abstract: The empirical Bayes test problem is considered for scale parameter of two-parameter exponential distribution under type-II censored data. By using wavelets estimation method, the EB test function is constructed, of which the asymptotic optimality and convergence rates are obtained. Finally, an example concerning the main result is given.

Key words: two-parameter exponential distribution, wavelets estimation, empirical Bayes test, asymptotic optimality, convergence rates