Estimation in surveys using conditional inclusion probabilities: Simple random sampling

In survey sampling, auxiliary information on the population is often availa ble, 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 c onditionally unbiased estimator. Four estimators that have a small conditio nal 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 samplin g 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 c an be viewed as an approximation of an application of the conditional princ iple.