Abstract
Lawrence R. Ernst (1995) "Maximizing
the Overlap of Sample Units for Two Designs with Simultaneous
Selection," Journal of Official Statistics.
It is demonstrated, using transportation theory, that
controlled selection can be used to solve the following
sampling problem. Sample units are to be selected with
probability proportional to size for two designs, both one
unit per stratum, denoted as D1 and D2, with generally
different stratifications. The goal of the problem is to
simultaneously select the sample units for the two designs in
a manner which maximizes the expected number of units that
are in both samples. The procedure differs from previous
overlap procedures in that it yields a better overlap, but is
only applicable when the two samples can be selected
simultaneously. An important special case occurs when the
probability of selection for each unit in D1 does not exceed
its probability of selection in D2. The procedure can then
guarantee that the D1 sample units are a subset of the D2
sample units. A proposed, but since canceled, expansion of
the Current Population Survey, which is discussed, would have
been a potential application of this special case. Variance
formulas for estimators of total under the controlled
selection procedure are also presented. In addition, it is
demonstrated that the procedure can easily be modified to
minimize expected overlap instead of maximizing it.
Last Modified Date: July 19, 2008
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