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

摘要

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