POWER APPROXIMATIONS TO AND POWER COMPARISON OF SMOOTH GOODNESS-OF-FIT TESTS

Global power approximations are presented for smooth goodness-of-fit t ests of a simple hypothesis, including e.g. Neyman's tests. The result ing approximation is in terms of a linear combination of non-central c hi-squares. A computationally easier further approximation is based on a single non-central chi-square distribution. The accuracy is illustr ated by numerical results. The test statistics are determined by the c hoice of an orthonormal system and the number of involved components. A criterion is proposed for comparison of the tests. The criterion may also be applied in other situations where (non-central) chi-square di stributions occur. The method is illustrated by numerical results.