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November, 1983 Independence Via Uncorrelatedness Under Certain Dependence Structures
Kumar Joag-Dev
Ann. Probab. 11(4): 1037-1041 (November, 1983). DOI: 10.1214/aop/1176993452


A characterization of independence via uncorrelatedness is shown to hold for the families satisfying positive and negative dependence conditions. For the associated random variables, the bounds on covariance functions obtained by Lebowitz (Comm. Math. Phys. $\mathbf{28}$ (1972), 313-321) readily yield such a characterization. An elementary proof for the same characterization is also given for a condition weaker than association, labeled as "strong positive (negative) orthant dependence." This condition is compared with the "linear positive dependence," under which Newman and Wright (Ann. Probab. $\mathbf{9}$ (1981), 671-675) obtained the characterization.


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Kumar Joag-Dev. "Independence Via Uncorrelatedness Under Certain Dependence Structures." Ann. Probab. 11 (4) 1037 - 1041, November, 1983.


Published: November, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0542.62046
MathSciNet: MR714966
Digital Object Identifier: 10.1214/aop/1176993452

Primary: 62E10
Secondary: 62H10

Keywords: Association positive and negative , characterization of independence , linear positive dependence , strong positive (negative) orthant dependence , uncorrelatedness

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 4 • November, 1983
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