Displaying similar documents to “Generalized covariance inequalities”

The empirical distribution function for dependent variables: asymptotic and nonasymptotic results in 𝕃 p

Jérôme Dedecker, Florence Merlevède (2007)

ESAIM: Probability and Statistics

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Considering the centered empirical distribution function as a variable in 𝕃 p ( μ ) , we derive non asymptotic upper bounds for the deviation of the 𝕃 p ( μ ) -norms of as well as central limit theorems for the empirical process indexed by the elements of generalized Sobolev balls. These results are valid for a large class of dependent sequences, including non-mixing processes and some dynamical systems.

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...