Consider a testing problem which is invariant under a group G of transformations of the sample space, and let C be a class of tests which is closed under G, so that C implies g C, where g is the test defined by g(x) (gx) If there exists an a e unique UMP member 0 of C, then 0 is almost invariant ...

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Consider a testing problem which is invariant under a group G of transformations of the sample space,

Question:

Consider a testing problem which is invariant under a group G of transformations of the sample space, and let C be a class of tests which is closed under G, so that φ ∈ C implies φg ∈ C, where φg is the test defined by φg(x) = φ(gx). If there exists an a.e. unique UMP member φ0 of C, then φ0 is almost invariant.

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