ESTIMATING THE MEAN WITH KNOWN COEFFICIENT OF VARIATION

Searls in 1964 showed that when the coefficient of variation is known, the sample mean is dominated with respect to mean squared error by an improved estimator that makes use of that coefficient, In this articl e we illustrate that this is true for a general class of estimators. E xpressions for the minimum mean squared error and the relative efficie ncy are given for general distributions. The improvement, as measured by relative efficiency, is seen to be independent of the form of the d istribution.