A biobjective method for sample allocation in stratified sampling
E. Carrizosa, D. Romero Morales
The two main and contradicting criteria guiding sampling design
are accuracy of estimators and sampling costs. In stratified
random sampling, the sample size must be allocated to strata in
order to optimize both objectives.
In this note we address, following a biobjective methodology, this
allocation problem. A two-phase method is proposed to describe the
set of Pareto-optimal solutions of this nonlinear integer
biobjective problem. In the first phase, all supported
Pareto-optimal solutions are described via a closed formula, which
enables quick computation. Moreover, for the common case in which
sampling costs are independent of the strata, all Pareto-optimal
solutions are shown to be supported. For more general cost
structures, the non-supported Pareto-optimal solutions are found
by solving a parametric knapsack problem.
The methods and results obtained in this paper are also extended to more
general settings, such as estimation problems with missing values and various
types of multi-response sampling.