Geodesic
Randomized goodness of fit tests
Kybernetika, Tome 47 (2011) no. 6, pp. 814-839.

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Classical goodness of fit tests are no longer asymptotically distributional free if parameters are estimated. For a parametric model and the maximum likelihood estimator the empirical processes with estimated parameters is asymptotically transformed into a time transformed Brownian bridge by adding an independent Gaussian process that is suitably constructed. This randomization makes the classical tests distributional free. The power under local alternatives is investigated. Computer simulations compare the randomized Cramér-von Mises test with tests specially designed for location-scale families, such as the Shapiro-Wilk and the Shenton-Bowman test for normality and with the Epps-Pulley test for exponentiality.
Classification : 62E20, 64E17
Keywords: goodness of fit tests with estimated parameters; Kolmogorov–Smirnov test; Cramér–von Mises test; randomization 
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     author = {Liese, Friedrich and Liu, Bing},
     title = {Randomized goodness of fit tests},
     journal = {Kybernetika},
     pages = {814--839},
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     number = {6},
     year = {2011},
     mrnumber = {2907844},
     zbl = {06047588},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2011__47_6_a1/}
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Liese, Friedrich; Liu, Bing. Randomized goodness of fit tests. Kybernetika, Tome 47 (2011) no. 6, pp. 814-839. http://geodesic.mathdoc.fr/item/KYB_2011__47_6_a1/