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TRUE/FALSE? With reasons For an estimator ? for ?, Rao-Blackwell Theorem states that Var (?(?|?)) ≤...

TRUE/FALSE? With reasons

For an estimator ? for ?, Rao-Blackwell Theorem states that Var (?(?|?)) ≤ ?ar(?) if and
only if ? is a sufficient statistic.

Math   Statistics-And-Probability   
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Answer #1

In our statement we are not given that our estimator is an unbiased estimator,

It is given any estimator which may be biased

So, the theorem become wrong in that case.

Hence, we conclude that the given statement is "false".

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