A Compromise Allocation Based on the Individual Mixed Allocations in Multivariate Stratified Sampling : A Goal Programming Approach

Abstract

Abtsrcat

In the literature of stratified random sampling Equal, Proportional, Optimum and several other allocations are well known. Usually any one type of allocation is selected and is applied to all the strata. But, there are practical situations in which some of the strata differ significantly in one or the other respect from others. In such situations the strata can be classified in mutually exclusive and exhaustive groups that favour a particular type of allocation. Different types of allocations may then be used in different groups. An allocation using the above criterion may be called a “Mixed Allocation”. In the present paper we considered a multivariate stratified population where more than one (say p) characteristics are defined on every unit of the population and developed a procedure to work out a compromise allocation that can be used for all characteristics under study. The problem of obtaining a compromise allocation is formulated as a Multiobjective Programming Problem that minimizes the deviation of all the sampling variances of the estimators of the p-population means from their respective optimum variances. The solution is obtained through Goal Programming Technique. A numerical example is also presented to illustrate the computational details.