Abstract
Larry Ernst and Christopher Guciardo (2002) "Allocating Sample to
Strata Proportional to Aggregate Measure of Size with Both Upper and Lower
Bounds on the Number of Units in Each Stratum."
For stratified PPS sampling, it is common to allocate the sample
among strata proportional to their aggregate measures of size. In some
cases, this allocation yields some strata whose sample sizes exceed
their frame sizes, in which case the sample sizes for these strata are
reduced to their frame sizes, and the remaining sample units are
allocated among the remaining strata proportional to their aggregate
measures of size. The process is repeated as necessary. An analogous
iterative procedure may be used if there are lower bounds on the number
of sample units in each stratum and these constraints are violated, but
the sample size does not exceed the frame size for any strata. However,
as explained in the paper, when the proportional allocation produces
both strata with sample sizes above upper bounds and strata with sizes
below lower bounds, an algorithm that sets the sample sizes for all
violating strata to their respective bounds does not lead to an optimal
allocation. An algorithm is presented that does yield an optimal
allocation. An application to the sample selection for the National
Compensation Survey is discussed.
Last Modified Date: March 19, 2003
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