In this chapter, we present properties of the GWSM. We will first show that the GWSM is unbiased for the estimation of the total Y B of the target population U B . We will then give the variance formula of the estimator Ŷ B , and we will discuss the estimation of this variance. Afterwards, we will show that, in the case where the indirect sampling carried out is conventional cluster sampling, the GWSM gives the same results as the classical theory. We will then deal with the case where we do a census of the population U A and where we do a census of the target population U B . We will also look at the use of weighted links. Finally, we will look to improve the estimator Ŷ B by reducing its variance. For this, we will first be using sufficient statistics, and next we will find optimum weights for the links.
KeywordsSimple Random Sampling Primary Sampling Unit Weighted Link Conditional Approach Adaptive Cluster Sampling
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