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On estimating the variance of a generalized Laplace distribution. (English) Zbl 0531.62028
Summary: When \(| X|^ k\) has a gamma distribution with parameters \(b^{- k}\) and \(k^{-1}\), H. Jakuszenkow [Demonstr. Math. 12, 581-591 (1979; Zbl 0443.62019)] has, for the loss function \(({\hat \theta}- \theta)^ 2\theta^{-2}\), considered the best multiple of \(\sum X^ 2_ i\) as an estimator of \(b^ 2\) and shown that it is Lehmann unbiased. In this paper, the best multiple of \((\sum | X_ i|^ k)^{2/k}\) is shown to be Lehmann unbiased, admissible and better than Jakuszenkow’s estimator.

MSC:
62F10 Point estimation
62C15 Admissibility in statistical decision theory
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References:
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