Statistical Uses of the Spatial Median

Abstract

SUMMARY The spatial median, called the mediancentre in an earlier paper by J. C. Gower, is defined as the bivariate location measure to minimize the sum of absolute distances to observations. its asymptotic efficiency relative to the sample mean vector with normal data is shown to exceed the usual univariate 2/π = 0.637. its estimating equations have an angular aspect and are used to develop “angle tests”, which are analogues of sign tests in one dimension.