Abstract
We consider the problem of multivariate multi-objective allocation where no or limited information is available within the stratum variance. Results show that a game theoretic approach (based on weighted goal programming) can be applied to sample size allocation problems. We use simulation technique to determine payoff matrix and to solve a minimax game.
Highlights
A choice of sampling plan is fundamental to any statistical study because it provides estimates of population parameters
Sample size allocation to each stratum is necessary in stratified random sampling design
The optimization technique can lead to misleading results because of limited information about cost and variance
Summary
A choice of sampling plan is fundamental to any statistical study because it provides estimates of population parameters. We propose a multivariate game theoretic approach for the sample size allocation problem in stratified random sampling design. The sampler objective is to minimizes his maximum (worst) value within the available budget, while allocating sample of size n to all strata. The optimal program consider all possible choices of sample, where adversary can choose his strategies independently. This implies for any strategy that the sampler would choose, as the Adversary will sample from every strata to maximize the model (6). Subject to 2 nh Nh >>>>>>; nh are integers; 8 h 1⁄4 1 and 2; ~nεn: We compute payoff matrix of sampler using equation below for various combinations of (n1, n2) that satisfy ~nεn s2jh 1⁄4
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