On the Attainment of the Cramer-Rao Bound in $\mathbb{L}_r$-Differentiable Families of Distributions
Muller-Funk, Ulrich ; Pukelsheim, Friedrich ; Witting, Hermann
Ann. Statist., Tome 17 (1989) no. 1, p. 1742-1748 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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 $P_\vartheta$.
Publié le : 1989-12-14
Classification:  Parametric families,  regular experiments,  62F10 
@article{1176347392,
     author = {Muller-Funk, Ulrich and Pukelsheim, Friedrich and Witting, Hermann},
     title = {On the Attainment of the Cramer-Rao Bound in $\mathbb{L}\_r$-Differentiable Families of Distributions},
     journal = {Ann. Statist.},
     volume = {17},
     number = {1},
     year = {1989},
     pages = { 1742-1748},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176347392}
}

Muller-Funk, Ulrich; Pukelsheim, Friedrich; Witting, Hermann. On the Attainment of the Cramer-Rao Bound in $\mathbb{L}_r$-Differentiable Families of Distributions. Ann. Statist., Tome 17 (1989) no. 1, pp.  1742-1748. http://gdmltest.u-ga.fr/item/1176347392/