A GLM has parameter with sufficient statistic S. A goodness-of-fit test statistic T has observed value

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A GLM has parameter β with sufficient statistic S. A goodness-of-fit test statistic T has observed value to. If β were known, a P-value is P = P(T ≥ to; β). Explain why P(T ≥ to | S) is the uniform minimum variance unbiased estimator of P.

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