最小方差无偏估计(UMVUE)
Recall
If is unbiased est's,
如果我們限定在無偏的估計方法中找最優的,那麼就是找方差最小的估計方法。也就是 Uniformly Minimum Variance Unbiased Estimator ,最小方差無偏估計。
危險
無偏並不一定是最好的。
Definition
is called UMVUE for iff
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i.e. unbiased.
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unbiased est. for ,
i.e. 方差最小。
Q: 充分統計量在估計上有什麼用?
Recall
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隨機變量
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If is suff for
since both and are independent of .
Theorem
Rao-Blackwellized
Suppse
be any est. for and is suff for , with
Let , then
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is a statistic with
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For any function ,
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If