Linearly independent set families Original Research Article

An apparently new definition of linearly independent set families in a linear space Rk is given (for short ‘independent set familiesʹ) and a relation of such families to families of separating hyperplanes is established. Independent set families are families of k subsets of the Rk defined by the property that any k points Pi, 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 ui of the Rk which are open and convex. The statistical application referred to is robust multilinear regression.