Geodesic
On the estimation theory of the scale parameter
Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 4, pp. 735-741

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The problem of estimating of the scale parameter $\sigma$ based on independent samples from the population with d.f. $F(x/\sigma)$ is considered. Under the condition (10) the following results are proved (Theorems 1 and 2). The estimator $c^\circ_n\bar x$ of $\sigma$ is admissible in the class of all estimators (or $\alpha_1^{-1}\bar x$ is admissible in the class of unbiased estimators) for any two values $n=n_1$, $n=n_2$, $n_2>n_1\ge3$, of the sample size if and only if $F(x)$ is either the degenerate d.f. or the d.f. of the Gamma-distribution. 
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     author = {A. M. Kagan and A. L. Rukhin},
     title = {On the estimation theory of the scale parameter},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {735--741},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {1967},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1967_12_4_a12/}
}
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A. M. Kagan; A. L. Rukhin. On the estimation theory of the scale parameter. Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 4, pp. 735-741. http://geodesic.mathdoc.fr/item/TVP_1967_12_4_a12/