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On the existence of locally mvu estimators

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  • D. Plachky

Abstract

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 θk+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.

Suggested Citation

  • D. Plachky, 1992. "On the existence of locally mvu estimators," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 46(4), pages 251-253, December.
    • Handle: RePEc:bla:stanee:v:46:y:1992:i:4:p:251-253
    DOI: 10.1111/j.1467-9574.1992.tb01343.x
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