Academic Journal
Measuring inequality in high dimensions: a Gini-based approach.
| Title: | Measuring inequality in high dimensions: a Gini-based approach. |
|---|---|
| Authors: | Auricchio, Gennaro1 (AUTHOR) gennaro.auricchio@unipd.it, Loli, Gabriele1 (AUTHOR), Toscani, Giuseppe1 (AUTHOR) |
| Source: | Statistics. Apr2026, Vol. 60 Issue 2, p291-310. 20p. |
| Subject Terms: | *Gini coefficient, *Scale invariance (Statistical physics), *Mathematical statistics, *Axioms, *Multivariate analysis, *Mathematical inequalities |
| Abstract: | While classical inequality indices – such as the Gini and pq-mean indices – satisfy a set of six desirable axiomatic properties in the univariate case (Hurley and Rickard. Comparing measures of sparsity. IEEE Trans Inf Theory. 2009;55(10):4723–4741. doi: ), extending these properties to the multivariate context poses a significant challenge, primarily due to the absence of a natural ordering in higher dimensions. Previous multivariate generalizations, although mathematically elegant, often lack interpretability and fail to preserve scale invariance. We analyze the approach proposed in Auricchio et al. (Extending the Gini index to higher dimensions via whitening processes. Rend Lincei. 2025;35(3):511–528), demonstrating that, under suitable conditions, it yields a multivariate Gini index that satisfies all six axioms and offers a practical, interpretable framework for measuring the unevenness of high-dimensional data. [ABSTRACT FROM AUTHOR] |
| Database: | Academic Search Index |
| FullText | Text: Availability: 0 CustomLinks: – Url: https://resolver.ebsco.com/c/fiv2js/result?sid=EBSCO:asx&genre=article&issn=02331888&ISBN=&volume=60&issue=2&date=20260401&spage=291&pages=291-310&title=Statistics&atitle=Measuring%20inequality%20in%20high%20dimensions%3A%20a%20Gini-based%20approach.&aulast=Auricchio%2C%20Gennaro&id=DOI:10.1080/02331888.2025.2557466 Name: Full Text Finder (for New FTF UI) (ns324271) Category: fullText Text: Full Text Finder MouseOverText: Full Text Finder |
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| Items | – Name: Title Label: Title Group: Ti Data: Measuring inequality in high dimensions: a Gini-based approach. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Auricchio%2C+Gennaro%22">Auricchio, Gennaro</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> gennaro.auricchio@unipd.it</i><br /><searchLink fieldCode="AR" term="%22Loli%2C+Gabriele%22">Loli, Gabriele</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Toscani%2C+Giuseppe%22">Toscani, Giuseppe</searchLink><relatesTo>1</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Statistics%22">Statistics</searchLink>. Apr2026, Vol. 60 Issue 2, p291-310. 20p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Gini+coefficient%22">Gini coefficient</searchLink><br />*<searchLink fieldCode="DE" term="%22Scale+invariance+%28Statistical+physics%29%22">Scale invariance (Statistical physics)</searchLink><br />*<searchLink fieldCode="DE" term="%22Mathematical+statistics%22">Mathematical statistics</searchLink><br />*<searchLink fieldCode="DE" term="%22Axioms%22">Axioms</searchLink><br />*<searchLink fieldCode="DE" term="%22Multivariate+analysis%22">Multivariate analysis</searchLink><br />*<searchLink fieldCode="DE" term="%22Mathematical+inequalities%22">Mathematical inequalities</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: While classical inequality indices – such as the Gini and pq-mean indices – satisfy a set of six desirable axiomatic properties in the univariate case (Hurley and Rickard. Comparing measures of sparsity. IEEE Trans Inf Theory. 2009;55(10):4723–4741. doi: ), extending these properties to the multivariate context poses a significant challenge, primarily due to the absence of a natural ordering in higher dimensions. Previous multivariate generalizations, although mathematically elegant, often lack interpretability and fail to preserve scale invariance. We analyze the approach proposed in Auricchio et al. (Extending the Gini index to higher dimensions via whitening processes. Rend Lincei. 2025;35(3):511–528), demonstrating that, under suitable conditions, it yields a multivariate Gini index that satisfies all six axioms and offers a practical, interpretable framework for measuring the unevenness of high-dimensional data. [ABSTRACT FROM AUTHOR] |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=asx&AN=192007283 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1080/02331888.2025.2557466 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 20 StartPage: 291 Subjects: – SubjectFull: Gini coefficient Type: general – SubjectFull: Scale invariance (Statistical physics) Type: general – SubjectFull: Mathematical statistics Type: general – SubjectFull: Axioms Type: general – SubjectFull: Multivariate analysis Type: general – SubjectFull: Mathematical inequalities Type: general Titles: – TitleFull: Measuring inequality in high dimensions: a Gini-based approach. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Auricchio, Gennaro – PersonEntity: Name: NameFull: Loli, Gabriele – PersonEntity: Name: NameFull: Toscani, Giuseppe IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 04 Text: Apr2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 02331888 Numbering: – Type: volume Value: 60 – Type: issue Value: 2 Titles: – TitleFull: Statistics Type: main |
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