10.18453/rosdok_id00005830 Liese, Friedrich Friedrich Liese http://d-nb.info/gnd/140883363 Liu, Bing Bing Liu http://d-nb.info/gnd/102958561X University of Rostock, Institute of Mathematics 2009 510 Mathematics 2009 en https://purl.uni-rostock.de/rosdok/id00005830 urn:nbn:de:gbv:28-rosdok_id00005830-1 Goodness of fi…t tests based on the empirical distribution function fail to be asymptotically distribution free if parameters are estimated. Asymptotically, the empirical process with estimated parameters is a centered Gaussian process with a covariance that di¤ers from the covariance function of the Brownian bridge. If the maximum likelihood estimator is used then the new covariance function is smaller, in the Loewner semiorder, than the covariance function of the Brownian bridge. Therefore one may transform the empirical process with estimated parameters back to a Brownian bridge by adding an independent process that is suitably constructed. Classical goodness of …t statistics have aftzer this transformation an asymptotic distribution as in the case of known parameters. The power under local alternatives of this new goodness of fit tests is studied and computer simulations compare the new test with their bootstrap versions.