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*.
Year of publication: |
1985
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Authors: | Arnold, Steven F. |
Published in: |
Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 3.1985, 5, p. 275-279
|
Publisher: |
Elsevier |
Subject: | invariance sufficiency |
Saved in:
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