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Optimum allocation in multivariate stratified survey as a problem of multiple criteria optimization. (Czech. English summary) Zbl 0611.62006

In the brief paper the problem of optimal allocation in multipurpose stratified sampling survey is studied from the point of view of multiple criteria optimization.
An account of previous solutions of the allocation problem for two or more stratifying variables shows that this surprisingly simple idea is an entirely new one. For the optimization the variances of sample estimates of the relevant variables are taken as the objective functions to be minimized on the set of admissible solutions given by the total sample size. If cost should be minimized too, the cost function may join the system of variance criteria.
The system of non-dominated solutions is shown to be the solution of the problem of optimal allocation in multivariate stratified survey. To find a single ”recommendable” allocation, an approximation of the ideal (non- admissible) solution of the optimization is recommended. Uniqueness of such an approximation is shown both theoretically and in an example.
Reviewer: J.Herzmann

MSC:

62D05 Sampling theory, sample surveys
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