Abstract
Alan Dorfman and Richard Valliant (1997)
"Stratification by Size Revisited."
Stratification is one of the most widely used techniques
in finite population sampling. Strata are disjoint
subdivisions of a population, the union of which exhaust the
universe, each of which contains a portion of the sample. Two
of its essential statistical purposes are to: (1) allow for
efficient estimation, especially in the case of
stratification by size, and (2) deal statistically with
subpopulations or domains by controlling their sample
allocations. Stratification by size is typically considered
as serving purpose (1) by creating strata in an efficient way
and optimally allocating the sample to the strata. Using
model-based analysis, we show that, in the situation where
stratification by size is generally used, optimal allocation
of a weighted balanced sample achieves exactly the same
variance as unstratified, best linear unbiased (BLU)
prediction coupled with weighted balanced sampling. In other
words, stratification by size has no advantage over the
optimal, unstratified procedure. This and other theoretical
findings are illustrated with simulations using real
populations.
Keywords: balanced sample, best linear unbiased predictor,
robustness, superpopulation model.
Last Modified Date: July 19, 2008
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