Geometrical Bounds for Variance and Recentered Moments
Geometrical Bounds for Variance and Recentered Moments
We bound the variance and other moments of a random vector based on the range of its realizations, thus generalizing inequalities of Popoviciu and of Bhatia and Davis concerning measures on the line to several dimensions. This is done using convex duality and (infinite-dimensional) linear programming. The following consequence of …