Median balls: An extension of the interquantile intervals to multivariate distributions

For a probability distribution on a Banach space. we introduce a family of central balls, indexed by their radius, using a proximity criterion close to those defining the spatial median. It is shown that these balls possess robustness and equivariance properties similar to those of the spatial median. They provide a multivariate generalization of the real interquantile intervals and can be interpreted as trimmed regions. (C) 1997 Academic Press.