Linearly independent set families

Abstract An apparently new definition of linearly independent set families in a linear space R k is given (for short `independent set families') and a relation of such families to families of separating hyperplanes is established. Independent set families are families of k subsets of the R k defined by the property that any k points P i , one from each subset, are linearly independent. The concept is not related to that of independent subsets of a finite basic set used in matroid theory. A typical example of an independent set family arising from a statistical application consists of congruent narrow cones around the unit vectors u i of the R k which are open and convex. The statistical application referred to is robust multilinear regression.