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Generalized minimax and maximin inequalities for order statistics and quantile functions


Author: Joel E. Cohen
Journal: Proc. Amer. Math. Soc. 141 (2013), 2515-2517
MSC (2010): Primary 62C20, 62G30, 90C47, 91A05, 97K40
Published electronically: February 28, 2013
MathSciNet review: 3043031
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ A$ be a finite real matrix with element $ A(i,j)$ in row $ i$ and
column $ j$. We generalize von Neumann's inequality $ \mathrm {min}_{j}\mathrm {max}_iA(i,j)\geq $
$ \mathrm {max}_i \mathrm {min}_j A(i,j)$ by replacing $ \mathrm {min}$ by every order statistic.


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Additional Information

Joel E. Cohen
Affiliation: Laboratory of Populations, The Rockefeller University and Columbia University, 1230 York Avenue, New York, New York 10065
Email: cohen@rockefeller.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11509-1
Keywords: Inequalities, minimax, maximin, order statistics, quantile functions
Received by editor(s): June 14, 2011
Received by editor(s) in revised form: October 11, 2011
Published electronically: February 28, 2013
Communicated by: Walter Craig
Article copyright: © Copyright 2013 Joel E. Cohen