“Rao–Blackwell theorem”的概念、定义、翻译、参考文献-科学参考

Rao–Blackwell theorem

Statistics

A theorem, proved independently by Rao in 1945 and Blackwell in 1947. Let {X_i} be independent identically distributed random variables with θ being an unknown parameter of their common probability distribution. The theorem states that, if T and S are two functions of the {X_i}, with T being an unbiased estimator of θ, and S being a sufficient statistic, then, for all θ, the expected value of T given S is an unbiased estimator of θ with variance never greater than that of T.

单词	Rao–Blackwell theorem
释义	Rao–Blackwell theorem Statistics A theorem, proved independently by Rao in 1945 and Blackwell in 1947. Let {X_i} be independent identically distributed random variables with θ being an unknown parameter of their common probability distribution. The theorem states that, if T and S are two functions of the {X_i}, with T being an unbiased estimator of θ, and S being a sufficient statistic, then, for all θ, the expected value of T given S is an unbiased estimator of θ with variance never greater than that of T.
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