Maurice Fréchet statisticien, enquêteur et agitateur public. (Maurice Fréchet statistician, investigator and public agitator). (French) Zbl 1053.01013

Armatte, Michel

Rev. Hist. Math. 7, No. 1, 7-65 (2001).

Summary: The mathematician Maurice Fréchet (1878–1973) is well known for his contributions to analysis and topology, and particularly his works on metric and abstract spaces. His role, following Émile Borel and together with Paul Lévy, in the renaissance of the French school of probability theory has been amply studied. In this paper, Fréchet the statistician will be explored, in particular the campaign sustained from 1934 to 1936 at the International Institute of Statistics (IIS) against improper uses of the correlation coefficient. This campaign took the unusual form of a survey sent to colleagues all over the world as well as a series of papers, committee reports, and censure motions within the IIS. It sheds light on the difficulties of giving a mathematically sound foundation to one of the most elementary notions of mathematical statistics, at the key moment when it was developing into an autonomous scientific discipline. Moreover, correlation is a notion largely used as an instrument of proof in several domains of observational sciences. Maurice Fréchet did not disdain contributing his own stone to the building of these mathematical foundations via his work on the notion of distance. And, because he respected applied mathematics, he used the same surveying technique - and with the same pugnacity - to examine the consistency and relevance of other statistical methods, like the estimation of the parameters of a theoretical distribution and the application of mathematics to economic and social questions.

MSC:

01A70	Biographies, obituaries, personalia, bibliographies
62-03	History of statistics

Keywords:

Fréchet; statistics; probability; correlation; distance; history; inquiry; correspondence