Displaying similar documents to “Grüss-type bounds for the covariance of transformed random variables.”

Grüss-type bounds for covariances and the notion of quadrant dependence in expectation

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...

Negative dependence structures through stochastic ordering.

Abdul-Hadi N. Ahmed (1990)

Trabajos de Estadística

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Several new multivariate negative dependence concepts such as negative upper orthant dependent in sequence, negatively associated in sequence, right tail negatively decreasing in sequence and upper (lower) negatively decreasing in sequence through stochastic ordering are introduced. These concepts conform with the basic idea that if a set of random variables is split into two sets, then one is increasing whenever the other is decreasing. Our concepts are easily verifiable and enjoy many...

On Bernoulli decomposition of random variables and recent various applications

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.