Work

An exterior algebra approach to generalised variances and cross-covariances

Year: 2025

Type: article

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.

Source: Soft Computing

DOI: 10.1007/s00500-025-10600-4

Authors: Henry P. Wynn, Anatoly Zhigljavsky

Institutions: London School of Economics and Political Science, Cardiff University

Language: English

Topic: Probability and Statistical Research

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

OpenAlex ID: W4410833686