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Lower and upper covariance

(2008) ADVANCES IN SOFT COMPUTING. 48. p.323-330
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Abstract
We give a definition for lower and upper covariance in Walley's theory of imprecise probabilities (or coherent lower previsions) that is direct, i.e., does not refer to credal sets. It generalizes Walley's definition for lower and upper variance. Just like Walley's definition of lower and upper variance, our definition for lower and upper covariance is compatible with the credal set approach; i.e., we also provide a covariance envelope theorem. Our approach mirrors the one taken by Walley: we first reformulate the calculation of a covariance as an optimization problem and then generalize this optimization problem to lower and upper previsions. We also briefly discuss the still unclear meaning of lower and upper (co)variances and mention some ideas about generalizations to other central moments.
Keywords
central moment, covariance, envelope theorem, variance, theory of imprecise probabilities

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Chicago
Quaeghebeur, Erik. 2008. “Lower and Upper Covariance.” In Advances in Soft Computing, ed. D Dubois, MA Lubiano, H Prade, MA Gil, P Grzegorzewski, and O Hryniewicz, 48:323–330. Berlin, Germany: Springer.
APA
Quaeghebeur, E. (2008). Lower and upper covariance. In D Dubois, M. Lubiano, H. Prade, M. Gil, P. Grzegorzewski, & O. Hryniewicz (Eds.), ADVANCES IN SOFT COMPUTING (Vol. 48, pp. 323–330). Presented at the 4th International conference on Soft Methods in Probability and Statistics (SMPS 2008), Berlin, Germany: Springer.
Vancouver
1.
Quaeghebeur E. Lower and upper covariance. In: Dubois D, Lubiano M, Prade H, Gil M, Grzegorzewski P, Hryniewicz O, editors. ADVANCES IN SOFT COMPUTING. Berlin, Germany: Springer; 2008. p. 323–30.
MLA
Quaeghebeur, Erik. “Lower and Upper Covariance.” Advances in Soft Computing. Ed. D Dubois et al. Vol. 48. Berlin, Germany: Springer, 2008. 323–330. Print.
@inproceedings{445579,
  abstract     = {We give a definition for lower and upper covariance in Walley's theory of imprecise probabilities (or coherent lower previsions) that is direct, i.e., does not refer to credal sets. It generalizes Walley's definition for lower and upper variance. Just like Walley's definition of lower and upper variance, our definition for lower and upper covariance is compatible with the credal set approach; i.e., we also provide a covariance envelope theorem. Our approach mirrors the one taken by Walley: we first reformulate the calculation of a covariance as an optimization problem and then generalize this optimization problem to lower and upper previsions. We also briefly discuss the still unclear meaning of lower and upper (co)variances and mention some ideas about generalizations to other central moments.},
  author       = {Quaeghebeur, Erik},
  booktitle    = {ADVANCES IN SOFT COMPUTING},
  editor       = {Dubois, D and Lubiano, MA and Prade, H and Gil, MA and Grzegorzewski, P and Hryniewicz, O},
  isbn         = {9783540850267},
  issn         = {1615-3871},
  keyword      = {central moment,covariance,envelope theorem,variance,theory of imprecise probabilities},
  language     = {eng},
  location     = {Toulouse, France},
  pages        = {323--330},
  publisher    = {Springer},
  title        = {Lower and upper covariance},
  url          = {http://dx.doi.org/10.1007/978-3-540-85027-4\_39},
  volume       = {48},
  year         = {2008},
}

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