Bounding the support of a measure from its marginal moments

TL;DR

This paper develops a method to explicitly bound the support of a measure in Rn using its marginal moments, and provides a numerical scheme to find the minimal containing box.

Contribution

It introduces a hierarchy of generalized eigenvalue problems to compute support bounds from marginal moments, offering a new computational approach.

Findings

Explicit support bounds derived from moments.

Numerical scheme for minimal bounding box.

Applicable to measures in Rn.

Abstract

Given all moments of the marginals of a measure on Rn, one provides (a) explicit bounds on its support and (b), a numerical scheme to compute the smallest box that contains the support. It consists of solving a hierarchy of generalized eigenvalue problems associated with some Hankel matrices.