Estimating the Mean with Known Coefficient of Variation

Abstract

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 article we illustrate that this is true for a general class of estimators. Expressions for the minimum mean squared error and the relative efficiency are given for general distributions. The improvement, as measured by relative efficiency, is seen to be independent of the form of the distribution.

Key Words:

• Domination
• Minimum mean squared error
• Optimal estimator
• Relative efficiency
• Sample median
• Unbiased estimator