# 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

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topMartín 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 -

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