= Statistical invariance principle
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If sample transformations preserve the model and both hypotheses, the invariance principle restricts attention to tests whose decisions are unchanged by those transformations. Such tests are functions of a <maximal invariant>. In estimation, the analogous requirement is <equivariance>, accompanied by an invariant <loss function> so that risks transform compatibly. The principle respects symmetries; it does not by itself prove optimality among all unrestricted procedures.
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