New Goodness of Fit Tests Based on Stochastic EDF |
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| Authors: | Jianxin Zhao Xingzhong Xu Xiaobo Ding |
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| Institution: | 1. Military Operation Staff Room , Navy Submarine Academy , Qingdao, China;2. Department of Mathematics , Beijing Institute of Technology , Beijing, China jxzhao69@gmail.com;4. Department of Mathematics , Beijing Institute of Technology , Beijing, China;5. Institute of Applied Mathematics , Chinese Academy of Sciences , Beijing, China |
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| Abstract: | A new approach of randomization is proposed to construct goodness of fit tests generally. Some new test statistics are derived, which are based on the stochastic empirical distribution function (EDF). Note that the stochastic EDF for a set of given sample observations is a randomized distribution function. By substituting the stochastic EDF for the classical EDF in the Kolmogorov–Smirnov, Cramér–von Mises, Anderson–Darling, Berk–Jones, and Einmahl–Mckeague statistics, randomized statistics are derived, of which the qth quantile and the expectation are chosen as test statistics. In comparison to existing tests, it is shown, by a simulation study, that the new test statistics are generally more powerful than the corresponding ones based on the classical EDF or modified EDF in most cases. |
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| Keywords: | Anderson–Darling test Berk–Jones test Cramér–von Mises test Einmahl–Mckeague test Goodness of fit Kolmogorov–Smirnov test Stochastic empirical distribution function |
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