Optimal Compromise Allocation in Two-Stage and Stratified Two-Stage Sampling Designs for Multivariate Study

摘要

When two-stage and stratified two-stage sampling designs are to be used and more than one characteristic are under study, usually it is not possible to use the individual optimal allocation of first-stage and second-stage sampling units to each stage and to various strata for one reason or the other. In such situations some criterion is needed to work out an acceptable allocation which is optimal for all characteristics in some sense. Such an allocation may be called an optimal compromised allocation. In this paper we discuss the problems of determining the optimal compromise allocation in multivariate two-stage and multivariate stratified two-stage sampling. These problems are formulated as Nonlinear Programming Problems (NLPP). The NLPPs are then solved using Lagrange multiplier technique and explicit formulae are obtained for the optimum allocation of the first-stage and second-stage sampling units.