An exterior algebra approach to generalised variances and cross-covariances

Wynn, Henry P. and Zhigljavsky, Anatoly ORCID: https://orcid.org/0000-0003-0630-8279 2025. An exterior algebra approach to generalised variances and cross-covariances. Soft Computing 29 (8) , pp. 4247-4257. 10.1007/s00500-025-10600-4

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Abstract

It has been shown by Pronzato et al. (Bernoulli 23(4A):2617–2642, 2017; J Multivar Anal 168:276–289, 2018) that simplicial volumes formed by independent copies of random variables can be used to extend the definition of generalised variances. It is shown in this paper that exterior algebra is a natural environment in which to study these constructions. This is used to extend the formulation to covariances and correlations. The theory leads naturally to dispersion ordering, that is partial orderings in which one random variable is more disperse than another if one squared simplicial volume stochastically dominates the other.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Mathematics
Additional Information:	License information from Publisher: LICENSE 1: URL: http://creativecommons.org/licenses/by/4.0/, Type: open-access
Publisher:	Springer
ISSN:	1432-7643
Date of First Compliant Deposit:	18 June 2025
Date of Acceptance:	8 January 2025
Last Modified:	18 Jun 2025 10:45
URI:	https://orca.cardiff.ac.uk/id/eprint/179164

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