Abstract
We consider sampling a finite population in two phases with varying probabilities, choosing the first phase sample using known size measures and the second phase subsample therefrom utilizing, in addition, ascertained auxiliary variate-values for the initial sample. Properties are investigated for proposed generalized regression estimators for the population mean of a variable of interest with values observed only for the selected subsample. Referring to infinite sequences of finite populations with increasing sizes and postulating super-population models, lower bounds for asymptotic model-expected design-‘mean square errors’ for the estimators are derived and optimal model-based designs are characterized so as to attain these bounds.
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