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December, 1989 On the Attainment of the Cramer-Rao Bound in $\mathbb{L}_r$-Differentiable Families of Distributions
Ulrich Muller-Funk, Friedrich Pukelsheim, Hermann Witting
Ann. Statist. 17(4): 1742-1748 (December, 1989). DOI: 10.1214/aos/1176347392

Abstract

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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Ulrich Muller-Funk. Friedrich Pukelsheim. Hermann Witting. "On the Attainment of the Cramer-Rao Bound in $\mathbb{L}_r$-Differentiable Families of Distributions." Ann. Statist. 17 (4) 1742 - 1748, December, 1989. https://doi.org/10.1214/aos/1176347392

Information

Published: December, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0694.62012
MathSciNet: MR1026310
Digital Object Identifier: 10.1214/aos/1176347392

Subjects:
Primary: 62F10

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 4 • December, 1989
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