Document Type

Journal Article

Department/Unit

Department of Economics

Title

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

Language

English

Abstract

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 distributions that are QDE but not QD. Such results play important roles in decision making under uncertainty, and particularly in areas such as economics, finance, and insurance. © 2011 Versita Warsaw and Springer-Verlag Wien.

Keywords

Covariance bound, Cuadras representation, Grüss's inequality, Hoeffding representation, Quadrant dependence, Quadrant dependence in expectation

Publication Date

2011

Source Publication Title

Central European Journal of Mathematics

Volume

9

Issue

6

Start Page

1288

End Page

1297

Publisher

Springer Verlag

DOI

10.2478/s11533-011-0088-x

Link to Publisher's Edition

http://dx.doi.org/10.2478/s11533-011-0088-x

ISSN (print)

18951074

ISSN (electronic)

16443616

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