Abstract
Richard Valliant and James E. Gentle (1997)
"An Application Of Mathematical Programming To Sample
Allocation," Computational Statistics and Data Analysis.
The problem of sample allocation in multipurpose surveys
is complicated by the fact that an efficient allocation for
some estimates may be inefficient for others. There may also
be precision goals that must be met for certain estimates
plus constraints on costs and minimum sample sizes for strata
to permit variance estimation. These requirements lead to
formulating the allocation problem as one of mathematical
programming with an objective function and constraints that
are nonlinear in the sample size target variables. We discuss
a flexible approach for a two-stage sample allocation that
uses multicriteria optimization programming. Software was
developed to permit survey designers to easily explore
alternative problem formulations and to compare the resulting
allocations. The method is illustrated using a business
establishment survey that estimates the costs to employers of
providing wages and benefits to employees and the percentages
of employees that receive certain benefits.
Keywords: Nonlinear optimization; multicriteria programming;
two-stage sampling; variance component estimation.
Last Modified Date: July 19, 2008
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