A Multivariate Tchebycheff Inequality
Olkin, Ingram ; Pratt, John W.
Ann. Math. Statist., Tome 29 (1958) no. 4, p. 226-234 / Harvested from Project Euclid
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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.
Publié le : 1958-03-14
Classification:  
@article{1177706720,
     author = {Olkin, Ingram and Pratt, John W.},
     title = {A Multivariate Tchebycheff Inequality},
     journal = {Ann. Math. Statist.},
     volume = {29},
     number = {4},
     year = {1958},
     pages = { 226-234},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177706720}
}

Olkin, Ingram; Pratt, John W. A Multivariate Tchebycheff Inequality. Ann. Math. Statist., Tome 29 (1958) no. 4, pp.  226-234. http://gdmltest.u-ga.fr/item/1177706720/