Unbiased goodness-of-fit tests |
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Authors: | Jesse Frey |
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Institution: | Department of Mathematical Sciences, Villanova University, Villanova, PA 19085, USA |
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Abstract: | Familiar distribution-free goodness-of-fit tests like the Kolmogorov–Smirnov test are all biased tests. In this paper, we show how to compute the bias of any distribution-free goodness-of-fit test that corresponds to a distribution-free confidence band for the cumulative distribution function (CDF). The bias of the Kolmogorov–Smirnov test turns out to be smaller than the biases of other distribution-free goodness-of-fit tests. We also develop a method for obtaining unbiased goodness-of-fit tests, which can then be inverted to obtain unbiased confidence bands for the CDF. Interestingly, only a discrete set of levels are available for the unbiased tests. Our power comparisons show that while removing bias improves the power of a test at some alternatives, it does not improve the overall power properties of the test. |
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Keywords: | Anderson&ndash Darling test Bias Confidence band Kolmogorov&ndash Smirnov test Nonparametric likelihood Power |
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