The Minimaxity of the Mid P-value under Linear and Squared Loss Functions |
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Authors: | Ian Fellows |
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Institution: | 1. Department of Psychiatry , University of California, San Diego , San Diego , California , USA ifellows@ucsd.edu |
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Abstract: | The mid-p is defined as the sum of the probabilities of all outcomes more extreme than an observed value, plus half of the probabilities of all outcomes exactly as extreme. On the one hand, it offers greater power than the standard p-value, but on the other, tests based on the mid-p statistic may have greater Type I error than their nominal level. This article investigates the mid p-value's properties under the estimated truth paradigm, which views p-values as estimators of the truth. The mid-p is shown to minimize the maximum risk for one-sided and two-sided tests. |
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Keywords: | Estimated truth Mid-p Minimax estimator p-value Randomized testing |
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