@inproceedings{EQ-2008-SMPS,
author = {Quaeghebeur, Erik},
editor = {D. Dubois and M. A. Lubiano and H. Prade and M. A. Gil and P. Grzegorzewski and O. Hryniewicz},
title = {Lower and upper covariance},
booktitle = {Soft Methods for Handling Variability and Imprecision},
year = {2008},
venue = {Toulouse, France},
eventdate = {2008-09-08/2008-09-10},
eventtitle = {SMPS 2006: 4th International Conference on Soft Methods in Probability and Statistics},
series = {Advances in Soft Computing},
number = {48},
publisher = {Springer},
location = {Berlin, Germany},
issn = {1615-3871},
isbn = {978-3-540-85026-7},
pages = {323--330},
url = {http://hdl.handle.net/1854/LU-445579},
doi = {10.1007/978-3-540-85027-4_39}
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},
}