A comparison of several eatimators of the center of a symmetric distribution

Let be a sample from a symmetric population with center θo. Boulanger and van Eeden (1983) introduced a class of estimators of θo defined as a value of θ which minimizes a non-negative functional H of the pair where, for , with Fn (x) the empirical distribution function of the observations. In this paper Monte-Carlo methods are used to compare the small-sample variances of two such estimators with those of the mean, the median and the Hodges–Lehmann estimator. These comparisons are made for samples of size n=7(1)5 and for six different source distributions.