## On Efficient Iterative Estimation Algorithm Using Sample Counterpart of the Searles’ Normal Mean Estimator with Exceptionally Large But Unknown Coefficient of Variation

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

**Abstract:**
This paper addresses the issue of finding an optimal estimator of the normal population mean when the coefficient of variation is unknown but is expected to be exceptionally high, as per the pilot surveys of the population at hand. The paper proposes an “Efficient Iterative Estimation Algorithm Using Sample Counterpart of the Searles’ Normal Mean Estimator”. The estimators per this strategy have no close form, and hence are not amenable to an analytical study determining their relative efficiencies as compared to the usual unbiased sample mean estimator. Nevertheless, we examine these relative efficiencies of our estimators with respect to the usual unbiased estimator by means of an illustrative numerical empirical study. MATLAB 7.7.0.471 (R2008b) is used in programming this illustrative ‘Simulated Empirical Numerical Study’.
**Key Words: **
MVUE, MMSE, Complete Sufficient Statistic, Numerical Study

**Authors:**

Ashok Sahai, ashok@gmail.com

Winston A. Richards, ugu@psu.edu

Robin M. Antoine, rmantoine@hotmail.com

Raghunadh M. Acharya, ra_raghu@yahoo.com

**Editor:**
Ahmed H. Youssef, ahyoussef@hotmail.com

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