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March, 1958 A Multivariate Tchebycheff Inequality
Ingram Olkin, John W. Pratt
Ann. Math. Statist. 29(1): 226-234 (March, 1958). DOI: 10.1214/aoms/1177706720


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.


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Ingram Olkin. John W. Pratt. "A Multivariate Tchebycheff Inequality." Ann. Math. Statist. 29 (1) 226 - 234, March, 1958.


Published: March, 1958
First available in Project Euclid: 27 April 2007

zbMATH: 0085.35204
MathSciNet: MR93865
Digital Object Identifier: 10.1214/aoms/1177706720

Rights: Copyright © 1958 Institute of Mathematical Statistics

Vol.29 • No. 1 • March, 1958
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