Extension of Theorem 3.7.1. The conclusions of Theorem 3.7.1 remain valid if the density of a sufficient

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Extension of Theorem 3.7.1. The conclusions of Theorem 3.7.1 remain valid if the density of a sufficient statistic T (which without loss of generality will be taken to be X), say pθ(x), is STP3 and is continuous in x for each θ.

[The two properties of exponential families that are used in the proof of Theorem 3.7.1 are continuity in x and

(a) of the preceding problem.]

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Testing Statistical Hypotheses Volume I

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Authors: E.L. Lehmann, Joseph P. Romano

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Extension of Theorem 3.7.1. The conclusions of Theorem 3.7.1 remain valid if the density of a sufficient

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