The adaptive calibration of testing p-values |
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Authors: | Guimei Zhao Li Wang |
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Institution: | 1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, China;2. Department of Statistics, North China University of Technology, Beijing, China;3. School of Science, China University of Mining and Technology (Beijing), Beijing, China |
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Abstract: | AbstractIn statistical hypothesis testing, a p-value is expected to be distributed as the uniform distribution on the interval (0, 1) under the null hypothesis. However, some p-values, such as the generalized p-value and the posterior predictive p-value, cannot be assured of this property. In this paper, we propose an adaptive p-value calibration approach, and show that the calibrated p-value is asymptotically distributed as the uniform distribution. For Behrens–Fisher problem and goodness-of-fit test under a normal model, the calibrated p-values are constructed and their behavior is evaluated numerically. Simulations show that the calibrated p-values are superior than original ones. |
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Keywords: | Adaptive p-value calibration Behrens–Fisher problem Generalized p-value Goodness-of-fit test Posterior predictive p-value |
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