Estimation in Surveys Using Conditional Inclusion Probabilities: Simple Random Sampling

Yves Tillé

International Statistical Review, 1998, vol. 66, issue 3, 303-322

Abstract: In survey sampling, auxiliary information on the population is often available. The aim of this paper is to develop a method which allows one to take into account such auxiliary information at the estimation stage by means of conditional bias adjustment. The basic idea is to attempt to construct a conditionally unbiased estimator. Four estimators that have a small conditional bias with respect to a statistic are proposed. It is shown that many of the estimators used in the literature in the case of simple random sampling can be obtained by using this estimation principle. The problem of simple random sampling with replacement, poststratification, and adjustment of a 2 x 2 dimensional contingency table to marginal totals are discussed in the conditional framework. Finally it is shown that the regression estimator can be viewed as an approximation of an application of the conditional principle. Dans les enquetes par sondage, une information auxiliaire sur l'ensemble de la population est souvent disponible. Le but de cent aticle est de développer une méthode qui permet de prendre en compte cette information auxiliaire à l'étape de l'estimation au moyen d'un ajustement du biais conditionnel. L'idée de base estde tenter de constuire un estimateur sans biaisconditionnel. Quatre estimateurs ayant un faible biais conditionnel sont proposés. On montre ensuite que beaucoup d'estimateus présentés dans la littérature dans le cas du plan simple sans remise peuvent etre obtenus en utilisant ce principe d'estimation. Les problémes du sondage aléatoire simple avec remise, de la poststratification, de l'ajustement d'un tableau de contigence de dimension 2 × 2 sont discutés dans le contexte de l'estimation conditionnelle. Finalement on montre que l'estimateur par la régression peut etre obtenu en cherchant une approximation de ce principe conditionnel.

Date: 1998
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