Randomized goodness of fit tests. (English) Zbl 1274.62322

Summary: 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.


62G10 Nonparametric hypothesis testing
62E17 Approximations to statistical distributions (nonasymptotic)
62E20 Asymptotic distribution theory in statistics
62G30 Order statistics; empirical distribution functions


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