On the centennial anniversary of Gini’s theory of statistical relations
The formulation of a unitary methodology for the analysis of relationships between statistical characters stands as a landmark in the Gini contribution to theoretical statistics. On the occasion of the centennial anniversary of the appearance of his most original and important contributions to the s...
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| Published in | Metron (Rome) Vol. 75; no. 2; pp. 227 - 242 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Milan
Springer Milan
01.08.2017
Springer Nature B.V |
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| Online Access | Get full text |
| ISSN | 0026-1424 2281-695X |
| DOI | 10.1007/s40300-017-0108-0 |
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| Abstract | The formulation of a unitary methodology for the analysis of relationships between statistical characters stands as a landmark in the Gini contribution to theoretical statistics. On the occasion of the centennial anniversary of the appearance of his most original and important contributions to the subject, this paper aims at highlighting Gini’s proposals, by reformulating them in a language which suits the modern treatments of mathematical statistics. An effort is made to stress the precursory value of those proposals, and to mention in a precise way some of their most significant developments, in particular as far as metrics for spaces of probability distributions and studies about monotone dependence are concerned. |
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| AbstractList | The formulation of a unitary methodology for the analysis of relationships between statistical characters stands as a landmark in the Gini contribution to theoretical statistics. On the occasion of the centennial anniversary of the appearance of his most original and important contributions to the subject, this paper aims at highlighting Gini’s proposals, by reformulating them in a language which suits the modern treatments of mathematical statistics. An effort is made to stress the precursory value of those proposals, and to mention in a precise way some of their most significant developments, in particular as far as metrics for spaces of probability distributions and studies about monotone dependence are concerned. |
| Author | Regazzini, Eugenio Cifarelli, Donato Michele |
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| Cites_doi | 10.1080/01621459.1958.10501481 10.1007/BF00532695 10.1007/978-3-540-71050-9 10.1214/aos/1176345528 10.1214/aoms/1177700153 10.1017/CBO9780511755347 10.2307/1905812 10.1090/gsm/058 |
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| Keywords | Copula Statistical relation Connection Monotone dependence Fréchet class Dissimilarity (index of) Homophily (index of) |
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| References | Dall’AglioGDistributions with given marginals: the beginningsDepend. Model.201642372503581273 Gini, C.: Considerazioni sulle probabilità a posteriori e applicazioni al rapporto dei sessi nelle nascite umane (con un’appendice di L. Galvani). Studi Economico-Giuridici dell’Università di Cagliari3, 133–171 (1911) GiniCLe applicazioni induttive del calcolo delle probabilitàRivista di Politica Economica19645410591083 FréchetMAnciens et nouveaux indices de corrélation. Leur application au calcul des retardes économiquesEconometrica1947151301927110.2307/19058120030.17001 SpearmannCA footrule for measuring correlationBr. J. Psychol.1906289 VillaniCOptimal Transport2009BerlinSpringer10.1007/978-3-540-71050-91156.53003 AmbrosioLGigliNSavaréGGradient Flows in Metric Spaces and in the Space of Probability Measures2005BaselBirkhäuser1090.35002 Salvemini, T.: Sugli indici di omofilia. Atti della I Riunione Scientifica della Società Italiana di Statistica in Supplemento Statistico ai Nuovi Problemi di Politica. Storia ed Economia 5, 105–115 (1939) LandennaGLa dissomiglianzaStatistica195616215780408 ContiPOn some descriptive aspects of measures of monotone dependenceMetron199351436013375960828.62050 CassataFIl Fascismo Razionale (Corrado Gini fra Scienza e Politica)2006RomaCarocci StrassenVThe existence of probability measures with given marginalsAnn. Math. Stat.19653642343917743010.1214/aoms/11777001530135.18701 GiniCDi una misura della dissomiglianza tra due gruppi di quantità e delle sue applicazioni allo studio delle relazioni statistiche.Atti del R. Istituto Veneto di Scienze, Lettere e Arti191474185213 GiniCIndici di omofilia e di rassomiglianza e loro relazioni col coefficiente di correlazione e con indici di attrazione.Atti del R. Istituto Veneto di Scienze, Lettere e Arti191474583610 KruskalWHOrdinal measures of associationJ. Am. Stat. Assoc.19585381486110094110.1080/01621459.1958.105014810087.15403 NelsenRBAn Introduction to Copulas20062New YorkSpringer1152.62030 FréchetMSur les tableaux de corrélation dont les marges sont donnéesAnn. Univ. Lyon(A)1951145377495180045.22905 HoeffdingWMasstalovariate korrelations theorieSehr. Math. Inst. Univ. Berlin19405181233 GiniCSul criterio di concordanza tra due caratteriAtti del R. Istituto Veneto di Scienze, Lettere e Arti191575309331 Dall’AglioGSugli estremi dei momenti delle funzioni di ripartizione doppiaAnnali della Scuola Normale Superiore di Pisa1956103574815770073.14002 RisserRTraynardC-ELes Principes de la Statistique Mathématique, II Livre, (Deuxième edition)1958ParisGauthier-Villars0080.35305 SchweizerBWolffEFOn nonparametric measures of dependence for random variablesAnn. Stat.1981987988561929110.1214/aos/11763455280468.62012 CambanisSSimonsGStoutWInequalities for Ek(X,Y)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal{E}} k(X, Y)$$\end{document} when the marginals are fixedZ. Wahrscheinlichkeitstheorie verw. Gebiete19763628529442077810.1007/BF005326950325.60002 GiniCIl Sesso dal Punto di Vista Statistico. Le Leggi della Produzione dei Sessi1908MilanoSandron CastellanoVCorrado Gini: a memoirMetron1965243841968270131.00502 de FinettiBA proposito di “correlazione”Supplemento Statistico ai Nuovi Problemi di Politica, Storia ed Economia193734157 DudleyRMReal Analysis and Probability2002CambridgeCambridge University Press10.1017/CBO97805117553471023.60001 GiniCDi Una Misura delle Relazioni tra le Graduatorie di Due Caratteri: l’Indice di Cograduazione1914RomaCecchini GiniCIndici di concordanzaAtti del R. Istituto Veneto di Scienze, Lettere e Arti19167514191461 Monge, G.: Mémoire sur la théorie des déblais et des remblais. Histoire de l’Académie Royale des Sciences de Paris, pp. 666–705 (1781) GiniCNuovi contributi alla teoria delle relazioni statisticheAtti del R. Istituto Veneto di Scienze, Lettere e Arti19157419031942 Villani, C.: Topics in Optimal Transportation. Graduate Studies in Mathematics, vol. 58. AMS, Providence (2003) WassersteinLMarkov processes over denumerable products of spaces describing large systems of automataProbl. Inf. Transm.196954752314115 CifarelliDMRegazziniESome contributions to the theory of monotone dependenceCNR-IAM19909017 FréchetMGénéralités sur les Probabilités (Premier Livre). Variables Aléatoires1937ParisGauthier-Villors63.0490.03 DM Cifarelli (108_CR5) 1990; 90 L Ambrosio (108_CR1) 2005 C Gini (108_CR18) 1914; 74 S Cambanis (108_CR2) 1976; 36 C Gini (108_CR21) 1916; 75 C Spearmann (108_CR31) 1906; 2 R Risser (108_CR28) 1958 108_CR29 L Wasserstein (108_CR35) 1969; 5 F Cassata (108_CR3) 2006 G Dall’Aglio (108_CR7) 1956; 10 M Fréchet (108_CR12) 1947; 15 108_CR26 C Gini (108_CR22) 1964; 54 C Gini (108_CR16) 1914 G Landenna (108_CR25) 1956; 16 B Schweizer (108_CR30) 1981; 9 C Villani (108_CR34) 2009 B Finetti de (108_CR9) 1937; 3 C Gini (108_CR17) 1914; 74 RB Nelsen (108_CR27) 2006 RM Dudley (108_CR10) 2002 V Castellano (108_CR4) 1965; 24 V Strassen (108_CR32) 1965; 36 W Hoeffding (108_CR23) 1940; 5 G Dall’Aglio (108_CR8) 2016; 4 C Gini (108_CR14) 1908 108_CR15 WH Kruskal (108_CR24) 1958; 53 M Fréchet (108_CR13) 1951; 14 C Gini (108_CR20) 1915; 75 M Fréchet (108_CR11) 1937 108_CR33 P Conti (108_CR6) 1993; 51 C Gini (108_CR19) 1915; 74 |
| References_xml | – reference: CambanisSSimonsGStoutWInequalities for Ek(X,Y)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal{E}} k(X, Y)$$\end{document} when the marginals are fixedZ. Wahrscheinlichkeitstheorie verw. Gebiete19763628529442077810.1007/BF005326950325.60002 – reference: GiniCIndici di omofilia e di rassomiglianza e loro relazioni col coefficiente di correlazione e con indici di attrazione.Atti del R. Istituto Veneto di Scienze, Lettere e Arti191474583610 – reference: SchweizerBWolffEFOn nonparametric measures of dependence for random variablesAnn. Stat.1981987988561929110.1214/aos/11763455280468.62012 – reference: GiniCDi una misura della dissomiglianza tra due gruppi di quantità e delle sue applicazioni allo studio delle relazioni statistiche.Atti del R. Istituto Veneto di Scienze, Lettere e Arti191474185213 – reference: LandennaGLa dissomiglianzaStatistica195616215780408 – reference: RisserRTraynardC-ELes Principes de la Statistique Mathématique, II Livre, (Deuxième edition)1958ParisGauthier-Villars0080.35305 – reference: SpearmannCA footrule for measuring correlationBr. J. Psychol.1906289 – reference: AmbrosioLGigliNSavaréGGradient Flows in Metric Spaces and in the Space of Probability Measures2005BaselBirkhäuser1090.35002 – reference: HoeffdingWMasstalovariate korrelations theorieSehr. Math. Inst. Univ. Berlin19405181233 – reference: Dall’AglioGDistributions with given marginals: the beginningsDepend. Model.201642372503581273 – reference: NelsenRBAn Introduction to Copulas20062New YorkSpringer1152.62030 – reference: Dall’AglioGSugli estremi dei momenti delle funzioni di ripartizione doppiaAnnali della Scuola Normale Superiore di Pisa1956103574815770073.14002 – reference: de FinettiBA proposito di “correlazione”Supplemento Statistico ai Nuovi Problemi di Politica, Storia ed Economia193734157 – reference: FréchetMSur les tableaux de corrélation dont les marges sont donnéesAnn. Univ. Lyon(A)1951145377495180045.22905 – reference: GiniCNuovi contributi alla teoria delle relazioni statisticheAtti del R. Istituto Veneto di Scienze, Lettere e Arti19157419031942 – reference: KruskalWHOrdinal measures of associationJ. Am. Stat. Assoc.19585381486110094110.1080/01621459.1958.105014810087.15403 – reference: GiniCDi Una Misura delle Relazioni tra le Graduatorie di Due Caratteri: l’Indice di Cograduazione1914RomaCecchini – reference: Gini, C.: Considerazioni sulle probabilità a posteriori e applicazioni al rapporto dei sessi nelle nascite umane (con un’appendice di L. Galvani). Studi Economico-Giuridici dell’Università di Cagliari3, 133–171 (1911) – reference: Villani, C.: Topics in Optimal Transportation. Graduate Studies in Mathematics, vol. 58. AMS, Providence (2003) – reference: ContiPOn some descriptive aspects of measures of monotone dependenceMetron199351436013375960828.62050 – reference: GiniCIl Sesso dal Punto di Vista Statistico. Le Leggi della Produzione dei Sessi1908MilanoSandron – reference: DudleyRMReal Analysis and Probability2002CambridgeCambridge University Press10.1017/CBO97805117553471023.60001 – reference: CifarelliDMRegazziniESome contributions to the theory of monotone dependenceCNR-IAM19909017 – reference: GiniCIndici di concordanzaAtti del R. Istituto Veneto di Scienze, Lettere e Arti19167514191461 – reference: StrassenVThe existence of probability measures with given marginalsAnn. Math. Stat.19653642343917743010.1214/aoms/11777001530135.18701 – reference: CassataFIl Fascismo Razionale (Corrado Gini fra Scienza e Politica)2006RomaCarocci – reference: Monge, G.: Mémoire sur la théorie des déblais et des remblais. Histoire de l’Académie Royale des Sciences de Paris, pp. 666–705 (1781) – reference: Salvemini, T.: Sugli indici di omofilia. Atti della I Riunione Scientifica della Società Italiana di Statistica in Supplemento Statistico ai Nuovi Problemi di Politica. Storia ed Economia 5, 105–115 (1939) – reference: FréchetMGénéralités sur les Probabilités (Premier Livre). Variables Aléatoires1937ParisGauthier-Villors63.0490.03 – reference: GiniCSul criterio di concordanza tra due caratteriAtti del R. Istituto Veneto di Scienze, Lettere e Arti191575309331 – reference: CastellanoVCorrado Gini: a memoirMetron1965243841968270131.00502 – reference: GiniCLe applicazioni induttive del calcolo delle probabilitàRivista di Politica Economica19645410591083 – reference: FréchetMAnciens et nouveaux indices de corrélation. Leur application au calcul des retardes économiquesEconometrica1947151301927110.2307/19058120030.17001 – reference: WassersteinLMarkov processes over denumerable products of spaces describing large systems of automataProbl. Inf. Transm.196954752314115 – reference: VillaniCOptimal Transport2009BerlinSpringer10.1007/978-3-540-71050-91156.53003 – volume: 75 start-page: 309 year: 1915 ident: 108_CR20 publication-title: Atti del R. Istituto Veneto di Scienze, Lettere e Arti – volume: 74 start-page: 583 year: 1914 ident: 108_CR18 publication-title: Atti del R. Istituto Veneto di Scienze, Lettere e Arti – volume-title: An Introduction to Copulas year: 2006 ident: 108_CR27 – volume-title: Il Fascismo Razionale (Corrado Gini fra Scienza e Politica) year: 2006 ident: 108_CR3 – volume: 90 start-page: 17 year: 1990 ident: 108_CR5 publication-title: CNR-IAM – volume: 3 start-page: 41 year: 1937 ident: 108_CR9 publication-title: Supplemento Statistico ai Nuovi Problemi di Politica, Storia ed Economia – volume: 53 start-page: 814 year: 1958 ident: 108_CR24 publication-title: J. Am. Stat. Assoc. doi: 10.1080/01621459.1958.10501481 – volume: 5 start-page: 181 year: 1940 ident: 108_CR23 publication-title: Sehr. Math. Inst. Univ. Berlin – volume: 36 start-page: 285 year: 1976 ident: 108_CR2 publication-title: Z. Wahrscheinlichkeitstheorie verw. Gebiete doi: 10.1007/BF00532695 – volume: 51 start-page: 43 year: 1993 ident: 108_CR6 publication-title: Metron – volume: 24 start-page: 3 year: 1965 ident: 108_CR4 publication-title: Metron – volume-title: Optimal Transport year: 2009 ident: 108_CR34 doi: 10.1007/978-3-540-71050-9 – volume: 9 start-page: 879 year: 1981 ident: 108_CR30 publication-title: Ann. Stat. doi: 10.1214/aos/1176345528 – volume: 36 start-page: 423 year: 1965 ident: 108_CR32 publication-title: Ann. Math. Stat. doi: 10.1214/aoms/1177700153 – volume-title: Di Una Misura delle Relazioni tra le Graduatorie di Due Caratteri: l’Indice di Cograduazione year: 1914 ident: 108_CR16 – ident: 108_CR29 – volume: 4 start-page: 237 year: 2016 ident: 108_CR8 publication-title: Depend. Model. – volume-title: Les Principes de la Statistique Mathématique, II Livre, (Deuxième edition) year: 1958 ident: 108_CR28 – volume-title: Généralités sur les Probabilités (Premier Livre). Variables Aléatoires year: 1937 ident: 108_CR11 – volume-title: Il Sesso dal Punto di Vista Statistico. Le Leggi della Produzione dei Sessi year: 1908 ident: 108_CR14 – volume-title: Real Analysis and Probability year: 2002 ident: 108_CR10 doi: 10.1017/CBO9780511755347 – volume-title: Gradient Flows in Metric Spaces and in the Space of Probability Measures year: 2005 ident: 108_CR1 – ident: 108_CR15 – volume: 74 start-page: 1903 year: 1915 ident: 108_CR19 publication-title: Atti del R. Istituto Veneto di Scienze, Lettere e Arti – volume: 2 start-page: 89 year: 1906 ident: 108_CR31 publication-title: Br. J. Psychol. – volume: 5 start-page: 47 year: 1969 ident: 108_CR35 publication-title: Probl. Inf. Transm. – volume: 16 start-page: 21 year: 1956 ident: 108_CR25 publication-title: Statistica – volume: 10 start-page: 35 year: 1956 ident: 108_CR7 publication-title: Annali della Scuola Normale Superiore di Pisa – volume: 15 start-page: 1 year: 1947 ident: 108_CR12 publication-title: Econometrica doi: 10.2307/1905812 – ident: 108_CR26 – ident: 108_CR33 doi: 10.1090/gsm/058 – volume: 75 start-page: 1419 year: 1916 ident: 108_CR21 publication-title: Atti del R. Istituto Veneto di Scienze, Lettere e Arti – volume: 54 start-page: 1059 year: 1964 ident: 108_CR22 publication-title: Rivista di Politica Economica – volume: 74 start-page: 185 year: 1914 ident: 108_CR17 publication-title: Atti del R. Istituto Veneto di Scienze, Lettere e Arti – volume: 14 start-page: 53 year: 1951 ident: 108_CR13 publication-title: Ann. Univ. Lyon(A) |
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| Title | On the centennial anniversary of Gini’s theory of statistical relations |
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