ON MULTIVARIATE MONOTONIC MEASURES OF LOCATION WITH HIGH BREAKDOWN POINT

SUMMARY. The purpose of this article is to propose a new scheme for robust multivariate ranking by introducing a not so familiar notion called monotonicity. Under this scheme, as in the case of classical outward ranking, we get an increasing sequence of regions diverging away from a central region (may be a single point) as nucleus. The nuclear region may be defined as the median region. Monotonicity seems to be a natural property which is not easily obtainable. Several standard statistics such weighted mean, coordinatewise median and the L\-median have been studied. We also present the geometry of constructing general monotonie measures of location in arbitrary dimensions and indicate its trade-off with other desirable properties. The article concludes with discussions on finite sample breakdown points and related issues.