A Proof for Lehmann-Scheffe Theorem

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A Proof for Lehmann-Scheffe Theorem. Kun Meng [email protected]. Department of Biostatistics. Brown University, Providence, RI, 02903, USA.
A Proof for Lehmann-Sche↵e Theorem Kun Meng [email protected] Department of Biostatistics Brown University, Providence, RI, 02903, USA

Lehmann-Sche↵e Theorem: Suppose that P is a family of populations, T is a sufficient and complete statistic for P, and ✓ is an estimable parameter functional on P. If S is an unbiased estimator of ✓, then EP (S|T ), which does not depend on the choice of P 2 P, is the unique UMVUE of ✓.

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