Question: 15. Envelope power function. Let S( a) be the class of all level-a tests of a hypothesis H, and let /3:(8) be the envelopepower function,

15. Envelope power function. Let S(

a) be the class of all level-a tests of a hypothesis H, and let /3:(8) be the envelopepower function, defined by /3:(8) = sup /3(8), ES

(a) where fJ denotes the power function of If the problem of testing H is invariant under a group G, then fJ:(8) is invariant under the induced group G. 1

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