Sufficiency and invariance
Suppose that a statistical decision problem is invariant under a group of transformations g [epsilon] G. T (X) is equivariant if there exists g* [epsilon] G* such that T(g(X)) = g*(T((X)). We show that the minimal sufficient statistic is equivalent and that if T(X) is an equivariant sufficient statistics and d(X) is invariant under G, then d*(T) = Ed(X)[short parallel]T is invariant under G*.
Volume (Year): 3 (1985)
Issue (Month): 5 (September)
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