Approximations to powers of phi-disparity goodness-of-fit tests

Abstract

The paper studies a class of tests based on disparities between the real-valued data and theoretical models resulting either from fixed partitions of the observation space, or from the partitions by the sample quantiles of fixed orders. In both cases there are considered the goodness-of-fit tests of simple and composite hypotheses. All tests are shown to be consistent, and their power is evaluated at the nonlocal as well as local alternatives.