Estimation in Surveys Using Conditional Inclusion Probabilities: Simple Random Sampling

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.

Calibration Estimation in Survey Sampling

“…Singh & Mohl (1996) compared several non‐negative regression type estimators through numerical examples. Using the idea of the conditional inclusion probabilities introduced by Tillé (1998), Park & Fuller (2005) introduced a set of regression weights that are positive in most samples. A more comprehensive overview of the calibration estimator can be found in Fuller (2002) and Särndal (2007).…”

Topics in Survey Sampling

“…Tille' (1995Tille' ( , 1998 proposed a general method based on conditional inclusion probabilities that allows one to construct directly an estimator with a small conditional bias with respect to a statistic.…”

“…Hence, write an approximate expression for the conditional weighted estimator of y. (Tille, 1998) 17. Conditionally Weighted Estimators Find conditionally weighted estimators of a finite population variance S; = L:~=1 (Yky)2 j(N -1) and study their properties with special emphasis on simple random sampling.…”

Regression estimation of the mean in survey sampling

“…A general estimator based on conditional inclusion probabilities was proposed by Tillé (1998) who constructed an estimator with a small conditional bias and showed that many classical estimators used in sample surveys can be derived from this general estimator. In section 3.2, we summarize results about the conditionally unbiased estimator and give some applications of the results based on Tillé (1998).…”

“…A general estimator based on conditional inclusion probabilities was proposed by Tillé (1998) who constructed an estimator with a small conditional bias and showed that many classical estimators used in sample surveys can be derived from this general estimator. In section 3.2, we summarize results about the conditionally unbiased estimator and give some applications of the results based on Tillé (1998). In the last section of this chapter, we in troduce a weighted regression estimator utilizing conditional inclusion probabilities and show that the weighted regression estimator in which the weights are a function of conditional in clusion probabilities is asymptotically equivalent to the regression estimator.…”