Abstract
We construct integral and supermum type goodness-of-fit tests for the family of power distribution functions. Test statistics are functionals of U-empirical processes and are based on the classical characterization of the power function distribution family belonging to Puri and Rubin. We describe the logarithmic large deviation asymptotics of test statistics under null-hypothesis and calculate their local Bahadur efficiency under common parametric alternatives. Conditions of local optimality of new statistics are given.
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