Hi everyone, the question is


Let \mathbb{U} be the set of all unbiased estimators of 0. Namely,

\mathbb{U}={ U(X): E_{\theta}(U(X)) = 0, for all \theta∈ \Omega}.
Then prove \delta(X) is an UMVUE of \theta iff for any U(X)∈ \mathbb{U}, Cov_{\theta}(\delta(X),(U(X)) = 0.
, and give a geometrical interpretation.
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I only figured that E_{\theta}(U(X)\delta(X))=0 so far, and I have no idea if I can use Lemann-Scheffe theorem to prove.
Please help me, and give some tips for me. Thx a lot!