Evaluation of some sampling strategies for finite populations using a continuous variable framework

This paper suggests an approach to the comparison of strategies for estimating the mean of a finite population under the heteroscedastic. regression model, y = θ(x + z), of the relationship between the variable of interest, y, anθ the auxiliary variable, x. A continuous variable framework is used as a model for the finite population. Two classes of estimators are considered, which include traditional approaches such as the Horvitz-Thompson estimator, the ratio estimator and the mean-of-the-ratios estimator. So-called best -unbiased estimators are also derived. The various strategies are evaluated in terms of their variance or mean square error, which is expressed as a function of four parameters; One population shape parameter, one sampling design parameter, and two parameters, k and g, specifying the error variance,var(z|x) = k2 xg. The various sampling strategies are studied with regard to their sensitivity to changes in these parameters.