## On Iterative Efficient Estimation Algorithm Using the Searls’ Normal Mean Estimator in the case of its Known Coefficient of Variation of the Normal Distribution

### by Ashok Sahai & Raghunadh M. Acharya .

**Abstract:**
This paper addresses the issue of finding an optimal estimator of the normal population mean when the coefficient of variation is known and is expected to be rather high, as per the pilot surveys of the population at hand. The paper proposes an “Efficient Iterative Estimation Algorithm, using computational statistics/intelligence, seminal to alterations of the Searles’ Normal Mean Estimator”. The ‘Relative Efficiency [as compared to the usual unbiased sample-mean estimator] estimators per this strategy have no simple algebraic form, and hence are not amenable to an analytical study determining their gainfulness, 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, using an illustrative simulation study with high replication. 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, sahai.ashok@gmail.com

Raghunadh, M. Acharya, Email2

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

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