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An estimator \(T^*\) is said to be an unbiased estimator of uniformly minimum variance, UMVUE, for \(\tau (\theta )\) if it satisfies \(\mathbb {E}_{\theta }[T^*]= \tau (\theta )\) \(\forall \theta \) and if \(\forall \) unbiased estimator T for \(\tau (\theta )\) , it holds: \(\displaystyle Var_{\theta }(T^*) \leq Var_{\theta }(T) \qquad \forall \theta . \)

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Uniform Minimum Variance Unbiased Estimators (UMVUEs)

  • 章节

  • 发表日期：

    2025年

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  • Francesca Gasperoni,
  • Francesca Ieva,
  • Anna Maria Paganoni

摘要

An estimator \(T^*\) is said to be an unbiased estimator of uniformly minimum variance, UMVUE, for \(\tau (\theta )\) if it satisfies \(\mathbb {E}_{\theta }[T^*]= \tau (\theta )\) \(\forall \theta \) and if \(\forall \) unbiased estimator T for \(\tau (\theta )\) , it holds: \(\displaystyle Var_{\theta }(T^*) \leq Var_{\theta }(T) \qquad \forall \theta . \)