Bounds on the Power for Some Renyi-Type Tests

Abstract

Let X 1 , X 2 , …, X n be a random sample from a random variable with continuous distribution function H ( x ). Renyi-type statistics, such as are considered for testing the hypothesis H ( x ) = F ( x ) against the class of alternatives G ( n ) ( x ), satisfying sup z ( F ( x ) — G ( n ) ( x )) Δ n > 0. Sharp bounds on the power, both for finite sample size and asymptotic values, are obtained for each of the tests examined, and these tests are shown consistent with respect to the class of alternatives considered.