Department of Economics
Grüss-type bounds for covariances and the notion of quadrant dependence in expectation
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.
Covariance bound, Cuadras representation, Grüss's inequality, Hoeffding representation, Quadrant dependence, Quadrant dependence in expectation
Source Publication Title
Central European Journal of Mathematics
Egozcue, Martín, Luis Fuentes García, Wing-Keung Wong, and Ričardas Zitikis. "Grüss-type bounds for covariances and the notion of quadrant dependence in expectation." Central European Journal of Mathematics 9.6 (2011): 1288-1297.