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Higher order asymptotics in estimation for two-sided Weibull type distributions

โœ Scribed by Masafumi Akahira; Kei Takeuchi

Publisher
Springer Japan
Year
1989
Tongue
English
Weight
759 KB
Volume
41
Category
Article
ISSN
0020-3157

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โœฆ Synopsis

We consider the estimation problem of a location parameter 0 on a sample of size n from a two-sided Weibull type densityf(x -0) = C(a) exp (-Ix-OI ยฐ) for -~<x<oo, -oo<0<oo and 1<a<3/2, where C(a) = a~ {2F(I / a)}. Then the bound for the distribution of asymptotically median unbiased estimators is obtained up to the 2a-th order, i.e., the order n t2~-11/2. The asymptotic distribution of a maximum likelihood estimator (MLE) is also calculated up to the 2a-th order. It is shown that the MLE is not 2a-th order asymptotically efficient. The amount of the loss of asymptotic information of the MLE is given.

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