The Theorems of Rao--Blackwell and Lehmann--Scheffe, Revisited

Authors: Hazhir Homei

It has been stated in the literature that for finding uniformly minimum-variance unbiased estimator through the theorems of Rao-Blackwell and Lehmann-Scheffe, the sufficient statistic should be complete; otherwise the discussion and the way of finding uniformly minimum-variance unbiased estimator should be changed, since the sufficiency assumption in the Rao-Blackwell and Lehmann-Scheffe theorems limits its applicability. So, it seems that the sufficiency assumptions should be expressed in a way that the uniformly minimum-variance unbiased estimator be derivable via the Rao-Blackwell and Lehmann-Scheffe theorems.

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[v1] 2019-04-18 03:53:13

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