Journal of Applied Mathematics & Bioinformatics

An Improved Minimum Mean Squared Error Estimate of the Square of the Normal Population Variance Using Computational Intelligence

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• Abstract

  Building upon the commonly-employed approach by Searls, substantial work has addressed the use of the known coefficient of the normal population mean and the normal population variance. Subsequently, several attempts have also sought to formulate estimators for the population mean and variance for a more probable case of the population coefficient of variation being unknown. Across numerous real-world applications within basic science, economic, and medical research, an analyst is required to have an efficient estimator of the square of the population variance. As such, the purpose of the current investigation was to develop and test a more efficient estimator of the square of the population variance for a normal distribution, beyond that of the Minimum Mean Squared Error (MMSE) for the square of the population variance. The proposed approach, which incorporated a metaheuristic optimization algorithm of Computational Intelligence in its derivation, captures the information in the sample more fully by including the sample coefficient of variation with the sample mean and sample variance. Results of an empirical simulation study found comprehensive improvement in the relative efficiency of the proposed estimator versus the MMSE estimator compared to the square of the sample variance across all defined sample sizes and population standard deviations.