P-values and e-values for non-parametric hypotheses with specified mean and variance
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We build natural one-sided p-values and e-values for four types of non-parametric composite hypotheses with specified mean and variance as well as other conditions on the shape of the data-generating distribution. These shape conditions include symmetry, unimodality, and their combination. The baseline p-variable is roughly improved by a multiplicative factor of 1/2 when assuming symmetry, 4/9 when assuming unimodality, 2/9 when assuming both. The baseline e-variable is improved by multiplicative factors of 2, 1 and 2, respectively.
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