Model assisted survey sampling strategy in two phases

Postulating a super-population regression model connecting a size variable, a cheaply measurable variable and an expensively observable variable of interest, an asymptotically optimal double sampling strategy to estimate the survey population total of the third variable is specified. To render it practicable, unknown model-parameters in the optimal estimator are replaced by appropriate statistics. The resulting generalized regression estimator is then shown to have a model-cum-asymptotic design based expected square error equal to that of the asymptotically optimum estimator itself. An estimator for design variance of the estimator is also proposed.