A Multivariate Tchebycheff Inequality
A multivariate Tchebycheff inequality is given, in terms of the covariances of the random variables in question, and it is shown that the inequality is sharp, i.e., the bound given can be achieved. This bound is obtained from the solution of a certain matrix equation and cannot be computed easily in general. Some properties of the solution are given, and the bound is given explicitly for some special cases. A Less sharp but easily computed and useful bound is also given.
Permanent link to this document: http://projecteuclid.org/euclid.aoms/1177706720
Digital Object Identifier: doi:10.1214/aoms/1177706720
Mathematical Reviews number (MathSciNet): MR93865
Zentralblatt MATH identifier: 0085.35204