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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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