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Sufficiency and invariance

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  • Arnold, Steven F.

Abstract

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*.

Suggested Citation

  • Arnold, Steven F., 1985. "Sufficiency and invariance," Statistics & Probability Letters, Elsevier, vol. 3(5), pages 275-279, September.
    • Handle: RePEc:eee:stapro:v:3:y:1985:i:5:p:275-279
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    Cited by:

    1. R. N. Rattihalli, 2023. "A Class of Multivariate Power Skew Symmetric Distributions: Properties and Inference for the Power-Parameter," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1356-1393, August.
    2. William P. Fisher Jr., 2023. "Separation Theorems in Econometrics and Psychometrics: Rasch, Frisch, Two Fishers and Implications for Measurement," Journal of Interdisciplinary Economics, , vol. 35(1), pages 29-60, January.

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    Keywords

    invariance sufficiency;

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