Multivariate Gini-type discrepancies
Auricchio G, Brigati G, Giudici P, Toscani G. 2025. Multivariate Gini-type discrepancies. Mathematical Models and Methods in Applied Sciences., 1–30.
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Author
Auricchio, Gennaro;
Brigati, GiovanniISTA;
Giudici, Paolo;
Toscani, Giuseppe
Department
Abstract
Measuring distances in a multidimensional setting is a challenging problem, which appears in many fields of science and engineering. In this paper, to measure the distance between two multivariate distributions, we introduce a new measure of discrepancy which is scale invariant and which, in the case of two independent copies of the same distribution, and after normalization, coincides with the scaling invariant multidimensional version of the Gini index recently proposed in [P. Giudici, E. Raffinetti and G. Toscani, Measuring multidimensional inequality: A new proposal based on the Fourier transform, preprint (2024), arXiv:2401.14012 ]. A byproduct of the analysis is an easy-to-handle discrepancy metric, obtained by application of the theory to a pair of Gaussian multidimensional densities. The obtained metric does improve the standard metrics, based on the mean squared error, as it is scale invariant. The importance of this theoretical finding is illustrated by means of a real problem that concerns measuring the importance of Environmental, Social and Governance factors for the growth of small and medium enterprises.
Publishing Year
Date Published
2025-04-01
Journal Title
Mathematical Models and Methods in Applied Sciences
Publisher
World Scientific Publishing
Page
1-30
ISSN
eISSN
IST-REx-ID
Cite this
Auricchio G, Brigati G, Giudici P, Toscani G. Multivariate Gini-type discrepancies. Mathematical Models and Methods in Applied Sciences. 2025:1-30. doi:10.1142/s0218202525500174
Auricchio, G., Brigati, G., Giudici, P., & Toscani, G. (2025). Multivariate Gini-type discrepancies. Mathematical Models and Methods in Applied Sciences. World Scientific Publishing. https://doi.org/10.1142/s0218202525500174
Auricchio, Gennaro, Giovanni Brigati, Paolo Giudici, and Giuseppe Toscani. “Multivariate Gini-Type Discrepancies.” Mathematical Models and Methods in Applied Sciences. World Scientific Publishing, 2025. https://doi.org/10.1142/s0218202525500174.
G. Auricchio, G. Brigati, P. Giudici, and G. Toscani, “Multivariate Gini-type discrepancies,” Mathematical Models and Methods in Applied Sciences. World Scientific Publishing, pp. 1–30, 2025.
Auricchio G, Brigati G, Giudici P, Toscani G. 2025. Multivariate Gini-type discrepancies. Mathematical Models and Methods in Applied Sciences., 1–30.
Auricchio, Gennaro, et al. “Multivariate Gini-Type Discrepancies.” Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2025, pp. 1–30, doi:10.1142/s0218202525500174.
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arXiv 2411.01052