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On the existence of locally mvu estimators
Author(s) -
Plachky D.
Publication year - 1992
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1992.tb01343.x
Subject(s) - mathematics , minimum variance unbiased estimator , estimator , bias of an estimator , u statistic , statistics , cauchy distribution , variance (accounting) , efficient estimator , stein's unbiased risk estimate , trimmed estimator , best linear unbiased prediction , distribution (mathematics) , unbiased estimation , bounded function , mathematical analysis , selection (genetic algorithm) , computer science , accounting , artificial intelligence , business
It is proved that there exists an unbiased estimator for some real parameter of a class of distributions, which has minimal variance for some fixed distribution among all corresponding unbiased estimators, if and. only if the corresponding minimal variances for all related unbiased estimation problems concerning finite subsets of the underlying family of distributions are bounded. As an application it is shown that there does not exist some unbiased estimator for θ k+c (ε≥0) with minimal variance for θ =0 among all corresponding unbiased estimators on the base of k i.i.d. random variables with a Cauchy‐distribution, where θ denotes some location parameter.