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Theory and methods: an optimal multivariate stratified sampling design using dynamic programming

Khan, Mohammad G.M. and Khan, E.A. and Ahsan, M.J. (2003) Theory and methods: an optimal multivariate stratified sampling design using dynamic programming. Australian and New Zealand Journal of Statistics, 45 (1). pp. 107-113. ISSN 1369-1473

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Numerous optimization problems arise in survey designs. The problem of obtaining an optimal (or near optimal) sampling design can be formulated and solved as a mathematical programming problem. In multivariate stratified sample surveys usually it is not possible to use the individual optimum allocations for sample sizes to various strata for one reason or another. In such situations some criterion is needed to work out an allocation which is optimum for all characteristics in some sense. Such an allocation may be called an optimum compromise allocation. This paper examines the problem of determining an optimum compromise allocation in multivariate stratified random sampling, when the population means of several characteristics are to be estimated. Formulating the problem of allocation as an all integer nonlinear programming problem, the paper develops a solution procedure using a dynamic programming technique. The compromise allocation discussed is optimal in the sense that it minimizes a weighted sum of the sampling variances of the estimates of the population means of various characteristics under study. A numerical example illustrates the solution procedure and shows how it compares with Cochran's average allocation and proportional allocation.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Technology and Environment (FSTE) > School of Computing, Information and Mathematical Sciences
Depositing User: Ms Mereoni Camailakeba
Date Deposited: 23 Apr 2003 08:19
Last Modified: 15 Mar 2017 22:12

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