A new approach to goodness-of-fit testing based on the integrated empirical process^*

Abstract

Abstract This paper takes a new approach to goodness-of-fit testing, based on Kolmogorov-Smirnov and Cramér-von Mises type functionals of the suitably integrated empirical process. A key limiting process is the integrated Brownian bridge. The new test statistics are compared with their classical "non-integrated" counterparts with respect to local Bahadur efficiency in case of shift alternatives. Whereas the integrated Kolmogorov-Smirnov test is locally Bahadur optimal for the logistic distribution, an integrated 1n-statistic turns out to be locally Bahadur optimal for the "root-logistic distribution". Keywords: Goodness-of-fit testintegrated empirical processintegrated Brownian bridgelarge deviationsBahadur efficiencylocal Bahadur optimalityAMS 1991 Subject Classifications: Primary: 62G10Secondary: 60G10Secondary: 62G20 *Work supported by the Deutsche Forschungsgemeinschaft and the Russian Foundation of Basic Research, grants No. 96-15-96199 and 98-01-0470. *Work supported by the Deutsche Forschungsgemeinschaft and the Russian Foundation of Basic Research, grants No. 96-15-96199 and 98-01-0470. Notes *Work supported by the Deutsche Forschungsgemeinschaft and the Russian Foundation of Basic Research, grants No. 96-15-96199 and 98-01-0470.