The legacy of Corrado Gini in survey sampling and inequality theory
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The legacy of Corrado Gini in survey sampling and inequality theory Yves Tillé1
Received: 26 October 2015 / Accepted: 25 May 2016 © Sapienza Università di Roma 2016
Abstract We present two seminal contributions of Corrado Gini on the theory of survey sampling and the theory of inequalities: the idea of balanced sampling and the Gini inequality index. These contributions have contributed to the development of a fertile field of research. Keywords Balanced sampling · Gini index · History of statistics · Variance estimation
1 Theory of survey sampling The 19th century can be viewed as the dark age of the theory of survey sampling because the prevalent conception of official statistics consisted of considering that only census data have scientific value. This paradigm was strongly defended by Adolphe Quetelet [53] when he wrote “la statistique n’a de valeur que par son exactitude” (“statistics only has a value by its exactitude”). In the 19th century, the theory of probability was already developed (see for example [41]). Nevertheless its use was generally limited to the adjustment of census data by distributions of probability. The paradigm of the complete enumeration was called into question by Kiaer [34–37] when he presented in Bern his work based on a “representative sample”. The papers of Kiaer have been the source of controversy that is related in the Bulletin de l’Institut International de Statistique (IIS). After the presentation of Kiaer, the “procès-verbal de l’Assemblée Générale de l’IIS,” 1896 [34] contains two very critical reactions: “M. V. Mayr: It is especially dangerous to come out in favor of this system of representative investigations in a meeting of statisticians. One can understand that for legislative or administrative purposes such enumeration can be useful—but we must not forget that it can never replace the complete statistical observation. It is especially necessary to support
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Yves Tillé [email protected] Institute of Statistics, University of Neuchâtel, rue de Bellevaux, 21, 2000 Neuchâtel, Switzerland
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that because among us in these days, there is a trend among the mathematicians in many directions who would calculate rather than observe. But we must stand firm and say no to computation where observation can be made.”1 “ Mr. Milliet: I think it is not fair that the Congress gives to the representative method (which finally may be an expedient) the importance that reliable statistics will never recognize. Doubtlessly statistics made with this method or, as I might call, statistics, pars pro toto, gave us here and there interesting information; but its principle is so in contradiction with the requirements of the statistical method, that, as statisticians, we must not give imperfect things the same rights of citizenship, so to speak, we set the ideal that scientifically we propose to achieve.”2 In 1924, a commission was created by the Bureau of the International Institute of Statistics (ISI) in order to assess the potential of the representative method. Corrado Gini
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