A procedure for computing optimal stratum boundaries and sample sizes for multivariate surveys

In most surveys, the target variables (items of interest) commonly resemble right-skewed distributions where the Stratified Random Sampling technique is used as a method of sampling and estimation. The methodology of constructing strata is called stratification. Over a particular characteristic chosen as the stratification variable (such as gender, geographical region, ethnicity, or any natural criteria), the survey may fail to form homogeneous strata - this would impact the precision in the estimates of the target variables. Stratification can lead to substantial improvements in the precision of sample estimators, which not only depends on the sample size, but also on the heterogeneity among the units of the population. The principal reason for stratification in the design of sample surveys is to reduce the variance of sample estimates. Surveys normally have more than one target variable with several variables both available and desirable for stratification. Stratification in such multivariate situations has not been explored to a great deal like the univariate case and requires algorithms to determine efficient stratum boundaries. This paper takes into consideration multiple survey variables and attempts to present a computational procedure to construct optimal stratum boundaries (OSB) using Dynamic Programming (DP) technique. A numerical example to determine the OSB for two main variables under study is also presented