An exterior algebra approach to generalised variances and cross-covariances

Wynn, Henry P. ORCID: 0000-0002-6448-1080 and Zhigljavsky, Anatoly (2025) An exterior algebra approach to generalised variances and cross-covariances. Soft Computing. ISSN 1432-7643

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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
Additional Information:	© 2025 The Authors
Divisions:	Statistics
Subjects:	Q Science > QA Mathematics
Date Deposited:	11 Jun 2025 14:54
Last Modified:	11 Jun 2025 16:03
URI:	http://eprints.lse.ac.uk/id/eprint/128357

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