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On the Attainment of the Cramer-Rao Bound in $\mathbb{L}_r$ -Differentiable Families of DistributionsOn the Attainment of the Cramer-Rao Bound in $\mathbb{L}_r$-Differentiable Families of Distributions

Ulrich Muller-Funk · Friedrich Pukelsheim · Hermann Witting刊期 1989-12-01 · 卷 17（4）The Annals of Statistics已编入正刊

Lᵣ可微分布族中Cramér–Rao下界的达到AI 解读

A rigorous proof is presented that global attainment of the Cramer-Rao bound is possible only if the underlying family of distributions is exponential. The proof is placed in the context of $\mathbb{L}_r(P_\vartheta)$ -differentiability, requiring strong differentiability in $\mathbb{L}_r(P_\vartheta)$ of the $r$ th root of the likelihood ratio relative to $P_\vartheta$ .A rigorous proof is presented that global attainment of the Cramer-Rao bound is possible only if the underlying family of distributions is exponential. The proof is placed in the context of $\mathbb{L}_r(P_\vartheta)$-differentiability, requiring strong differentiability in $\mathbb{L}_r(P_\vartheta)$ of the $r$th root of the likelihood ratio relative to $P_\vartheta$.

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被引 15 次 ↗OpenAlex · 核验 2026-10-04

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On the Attainment of the Cramer-Rao Bound in Lr\mathbb{L}_rLr​-Differentiable Families of DistributionsOn the Attainment of the Cramer-Rao Bound in $\mathbb{L}_r$-Differentiable Families of Distributions

On the Attainment of the Cramer-Rao Bound in $\mathbb{L}_r$ -Differentiable Families of DistributionsOn the Attainment of the Cramer-Rao Bound in $\mathbb{L}_r$-Differentiable Families of Distributions