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On Efficient Variance Estimators for Normal Population with known Coefficient of Variation

Ashok Sahai, Robin Antoine, Winston A. Richards, M. Raghunadh Acharya


This paper addresses the issue of finding an optimal estimator of the normal population variance using the known coefficient of variation. In this setup there is no complete sufficient statistic for the variance, hence Rao-Blackwellization is unavailable to us. Despite this, we have been able to obtain an estimator with minimum MSE, which is more efficient than other estimators in the literature. The proposed estimator may also be the MVUE, but we have not been able to confirm this. Lastly, we examine the relative efficiencies of our estimators with respect to the usual unbiased estimator S2 by means of a numerical empirical study.


MVUE, MMSE, Complete Sufficient Statistic, Numerical Study

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