Journal of Official Statistics, Vol.16, No.2, 2000. pp. 139–154
Stratification by Size Revisited
Alan H. Dorfman and Richard Valliant
Abstract:Stratification by size is used in finite population sampling as a means of producing efficient estimators. The technique has also been recognized as a method of approximating optimum selection probabilities for a variety of estimators. Using prediction theory, we show that an unstratified, weighted balanced sample yields the same variance as stratification by size with optimum allocation of a stratified, weighted balanced sample when using the best linear unbiased predictor of the population total. Stratification by size can, thus, be viewed as nothing more than a way of selecting a sample with overall weighted balance. A practical method of selecting weighted balanced samples is to use restricted randomization in which poorly balanced samples are rejected. We illustrate by simulation the superiority of weighted balanced sampling in three real populations.
Keywords:Balanced sample; best linear unbiased predictor; minimal model; restricted „random sampling; robustness; superpopulation model.
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