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

Martín Egozcue; Luis García; Wing-Keung Wong; Ričardas Zitikis

Open Mathematics (2011)

  • Volume: 9, Issue: 6, page 1288-1297
  • ISSN: 2391-5455

Abstract

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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 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.

How to cite

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Martín Egozcue, et al. "Grüss-type bounds for covariances and the notion of quadrant dependence in expectation." Open Mathematics 9.6 (2011): 1288-1297. <http://eudml.org/doc/269111>.

@article{MartínEgozcue2011,
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.},
author = {Martín Egozcue, Luis García, Wing-Keung Wong, Ričardas Zitikis},
journal = {Open Mathematics},
keywords = {Grüss’s inequality; Covariance bound; Quadrant dependence; Quadrant dependence in expectation; Hoeffding representation; Cuadras representation; covariance bound; quadrant dependence; quadrant dependence in expectation},
language = {eng},
number = {6},
pages = {1288-1297},
title = {Grüss-type bounds for covariances and the notion of quadrant dependence in expectation},
url = {http://eudml.org/doc/269111},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Martín Egozcue
AU - Luis García
AU - Wing-Keung Wong
AU - Ričardas Zitikis
TI - Grüss-type bounds for covariances and the notion of quadrant dependence in expectation
JO - Open Mathematics
PY - 2011
VL - 9
IS - 6
SP - 1288
EP - 1297
AB - 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.
LA - eng
KW - Grüss’s inequality; Covariance bound; Quadrant dependence; Quadrant dependence in expectation; Hoeffding representation; Cuadras representation; covariance bound; quadrant dependence; quadrant dependence in expectation
UR - http://eudml.org/doc/269111
ER -

References

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