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Teoriya Veroyatnostei i ee Primeneniya, 1967, Volume 12, Issue 4, Pages 735–741
(Mi tvp762)
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This article is cited in 4 scientific papers (total in 4 papers)
Short Communications
On the estimation theory of the scale parameter
A. M. Kagan, A. L. Rukhin Leningrad
Abstract:
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.
Received: 09.08.1966
Citation:
A. M. Kagan, A. L. Rukhin, “On the estimation theory of the scale parameter”, Teor. Veroyatnost. i Primenen., 12:4 (1967), 735–741; Theory Probab. Appl., 12:4 (1967), 672–678
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https://www.mathnet.ru/eng/tvp762 https://www.mathnet.ru/eng/tvp/v12/i4/p735
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Abstract page: | 363 | Full-text PDF : | 121 |
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