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For certain skewed populations there are biased estimators of the population mean, , which have smaller mean square error than the sample mean . This article investigates the properties of the square-root estimator , where . It is shown that this estimator can provide substantial gains in efficiency over when sampling from highly skewed populations. Graphs and tables are presented showing optimum values of C for various types of distributions and sample sizes, and illustrating that the precise distribution form need not be known in order to gain efficiency by using the square root estimator.
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Jenkins et al. (1973) studied this question.
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