The allocation of sample size into strata in stratified random sampling under nonlinear cost constraints

Determination of appropriate sampling method for the population structure and buget is one of the most important stages in researches. Although there are many kinds of sampling methods, the most widely used in the applications is stratified random sampling. The number of sample units will be selected from each stratum is one of the points must be taken into consideration when using stratified random sampling. Most of the studies in literature deal with the determination of the sample size that will be selected from the stratum under linear cost constraint. However in this study, nonlinear cost constraints were taken into consideration. Under nonlinear cost constraints, the sample size that should be selected from strata was determined for both univariate and multivariate stratified random sampling. The superiority of each optimization method under nonlinear cost constraints and structure of nonlinear cost constraints were investigated for the univariate stratified random sampling. As to multivariate stratified random sampling, a new model in which the structure within strata is reflected to the problem of allocation of sample size has been proposed in order to determine the sample size that will be selected from strata. A simulation study has been conducted in order to display the superiority of each optimization method in the univariate case and to compare the new proposed model with the classical model in the multivariate case.The results show that the new proposed model determines sample size that will be selected from strata better than the classical model.