Question

(Mathematical statistics)

5. Prove that if is a best unbiased estimator of parameter $\theta$ , then is unique.

Answer 1

firstnote that Rao-Blackwell give us the best unbiased estimator, therefore we will only show that it is unique using Rao-Blackwell theorem. the proof is as

in this by Ploe this in statement of Lehmonn - Scheffe the to prove this, we will use Rao - Block well this by this let if w' is any unbiased estimator of O, then Varese Erw'i wn is an unbiased estimate of . Var CEE wil wo) s vadw's, but Ecoles of wiso by completeness, it must conicide on per te w. therefore regaodress of the | particular value of O, 190/w) e Vaolo's csi suurim Yüni que o with Vance Ewl wil av in a p" of wiso by completen mScanner