Efficient Estimator of Population Variance of Normal Distribution with Known Coefficient of Variation

by Ashok Sahai.

Abstract: In case of the Normal distribution with a known coefficient of variation, the sufficient statistics (sample mean & sample variance) is not complete. In the absence of a complete sufficient statistics the “Rao-Blackwellization” is unavailable, and hence we are groping in dark about the most efficient estimators for population parameter. There is some research-literature on using the known coefficient of variation for efficient estimation of the normal population mean, and the normal population variance. In the present paper a successful attempt is made to propose an efficient estimator of population variance for such a normal distribution. As the comparisons or algebraically intricate otherwise, an empirical simulation study, using MATLAB 2010b code with 100001 replications, is carried out to bring forth the efficiency of the proposed estimator relative to the sample variance, which is the usual unbiased estimator of the population variance.

Key Words: Complete-sufficient statistic; Empirical-simulation study; Minimum mean-squared-error estimator

Ashok Sahai, sahai.ashok@gmail.com

Editor: Abd Allah Mohamed Abd Elfattah,a_afattah@hotmail.com

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