On the precision of an estimator of Mean for Domains in Double Sampling for Inclusion Probabilities

Abstract

In sample surveys, estimates are often required for small subclasses of the population under study. In many sample situations, the size of the domain and hence the number of sample units that fall in the domain are unknown before the start of the survey. In this paper, we examine the effect of the randomness of the domain size on the precision of an estimator for the domain under double sampling for inclusion probabilities. It is assumed that the population can be divided into different strata. The results show that there is a positive contribution to the variance of the estimator which varies from one stratum to another. This addition vanishes where the domain coincides with a stratum. The total sampling variance depends only on components of variance for the domain and is inversely related to the total sample size in each phase of the survey.
Key Words: Domain, Double Sampling, Unequal Probabilities.


(Global Journal of Mathematical Sciences: 2002 1 (1&2): 49-58)