Quasi-medians are robust and relatively efficient estimators of a common mean given multivariate normality

In this note we examine the efficiency of averaging marginal quasi-medians as compared to averaging marginal sample means when estimating a common location parameter given multivariate normal data. It is shown that the efficiency of certain quasi-medians approach that of the sample mean as the dimension of the problem grows larger. Modest gains in efficiency may be had even when the dimension of the problem is extended from the univariate setting to the bivariate setting.