Abstract
LetX andY be two experiments invariant with respect to an amenable measureable group. By a theorem of C. Boll which is proved with the help of a well-known fixed point theorem, the decision theoretical comparison relationX ≻Y introduced by LeCam can be characterized in terms of invariant Markov kernels. Applying this result to translation (invariant) experiments one obtains, an explicit analysis of the comparison relationship in the special case of Gaussian experiments.
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