Grüss-type bounds for the covariance of transformed random variables.
Egozcue, Martín, García, Luis Fuentes, Wong, Wing-Keung, Zitikis, Ričardas (2010)
Journal of Inequalities and Applications [electronic only]
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Egozcue, Martín, García, Luis Fuentes, Wong, Wing-Keung, Zitikis, Ričardas (2010)
Journal of Inequalities and Applications [electronic only]
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Sung, Soo Hak (2009)
Journal of Inequalities and Applications [electronic only]
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Căbulea, Lucia (2001)
Acta Universitatis Apulensis. Mathematics - Informatics
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Martín Egozcue, Luis García, Wing-Keung Wong, Ričardas Zitikis (2011)
Open Mathematics
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We show that Grüss-type probabilistic inequalities for covariances can be considerably sharpened when the underlying random variables are quadrant dependent in expectation (QDE). The herein established covariance bounds not only sharpen the classical Grüss inequality but also improve upon recently derived Grüss-type bounds under the assumption of quadrant dependency (QD), which is stronger than QDE. We illustrate our general results with examples based on specially devised bivariate...
Amini, M., Bozorgnia, A. (2000)
Journal of Applied Mathematics and Stochastic Analysis
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A. Yu. Zaitsev (1998)
ESAIM: Probability and Statistics
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Nadarajah, Saralees (2005)
Journal of Applied Mathematics
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Rio Emmanuel (1997)
ESAIM: Probability and Statistics
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Mark Veraar (2008)
Colloquium Mathematicae
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We obtain lower bounds for ℙ(ξ ≥ 0) and ℙ(ξ > 0) under assumptions on the moments of a centered random variable ξ. The estimates obtained are shown to be optimal and improve results from the literature. They are then applied to obtain probability lower bounds for second order Rademacher chaos.
Yeh, Cheh-Chih, Yeh, Hung-Wen, Chan, Wenyaw (2008)
Journal of Inequalities and Applications [electronic only]
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François Germinet (2007-2008)
Séminaire Équations aux dérivées partielles
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In this review, we first recall a recent Bernoulli decomposition of any given non trivial real random variable. While our main motivation is a proof of universal occurence of Anderson localization in continuum random Schrödinger operators, we review other applications like Sperner theory of antichains, anticoncentration bounds of some functions of random variables, as well as singularity of random matrices.