Asymptotic Comparison of Cramer-von Mises and Nonparametric Function Estimation Techniques for Testing Goodness-of-Fit

Abstract

Two new statistics for testing goodness-of-fit are derived from the viewpoint of nonparametric density estimation. These statistics are closely related to the Neyman smooth and Cramer-von Mises statistics but are shown to have superior properties both through asymptotic and small sample analyses. Comparison of the proposed tests with the Cramer-von Mises statistic requires the development of a novel technique for comparing tests that are capable of detecting local alternatives converging to the null at different rates.