Introduction

Abstract

The book introduces a new representation of probability measures — the lift zonoid representation — and demonstrates its usefulness in multivariate analysis. A measure on the Euclidean d-space is represented by a convex set in (d + 1)-space, its lift zonoid. This yields an embedding of the d-variate measures into the space of symmetric convex compacts in ℝ^d+1. The embedding map is positive homogeneous, additive, and continuous. It has many applications in data analysis as well as in inference and in the comparison of random vectors.