Читать книгу Sampling and Estimation from Finite Populations - Yves Tille - Страница 15

The report of the commission presented to the ISI Congress in 1925 marked the official recognition of the use of survey sampling. Most of the basic problems had already been posed, such as the use of random samples and the calculation of the variance of the estimators for simple and stratified designs. The acceptance of the use of partial data, and especially the recommendation to use random designs, led to a rapid mathematization of this theory. At that time, the calculation of probabilities was already known. In addition, statisticians had already developed a theory for experimental statistics. Everything was in place for the rapid progress of a fertile field of research: the construction of a statistical theory of survey sampling.

Jerzy Neyman (1894–1981) developed a large part of the foundations of the probabilistic theory of sampling for simple, stratified, and cluster designs. He also determined the optimal allocation of a stratified design. The optimal allocation method challenges the basic idea of the quota method, which is the “representativeness”. Indeed, depending on the optimal stratification, the sample should not be a miniature of the population as some strata must be overrepresented. The article published by Neyman (1934) in the Journal of the Royal Statistical Society is currently considered one of the founding texts of sampling theory. Neyman identified the main fields of research and his work was to have a very important impact in later years. We now know that Tschuprow (1923) had already obtained some of the results that were attributed to Neyman, but the latter seems to have found them independently of Tschuprow. It is not surprising that such a discovery was made simultaneously in several places. From the moment that the use of random samples was considered a valid method, the theory would arise directly from the application of the theory of probability.