On Sample Allocation in Multivariate Surveys

The problem of a sample allocation between strata in the case of multiparameter surveys is considered in this article. There are several multivariate sample allocation methods and, moreover, several criteria to deal with in such a case. A maximum coefficient of variation of estimators of the population mean of characters under study is taken as the optimality criterion. This article contains a study on a group of the methods that are easy to implement and do not need complex numerical computation; however, they all are approximate. Five such methods are presented and compared using a simulation study. Finally, it is shown which methods should be considered when designing a survey in which the multivariate sample allocation is to be involved.