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Theory & Methods: An Optimal Multivariate Stratified Sampling Design Using Dynamic Programming

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  • M.G.M. Khan
  • E.A. Khan
  • M.J. Ahsan

Abstract

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.

Suggested Citation

  • M.G.M. Khan & E.A. Khan & M.J. Ahsan, 2003. "Theory & Methods: An Optimal Multivariate Stratified Sampling Design Using Dynamic Programming," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 45(1), pages 107-113, March.
    • Handle: RePEc:bla:anzsta:v:45:y:2003:i:1:p:107-113
    DOI: 10.1111/1467-842X.00264
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    Cited by:

    1. Rahul Varshney & Najmussehar & M. Ahsan, 2012. "Estimation of more than one parameters in stratified sampling with fixed budget," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 75(2), pages 185-197, April.
    2. Rahul Varshney & M. Khan & Ummatul Fatima & M. Ahsan, 2015. "Integer compromise allocation in multivariate stratified surveys," Annals of Operations Research, Springer, vol. 226(1), pages 659-668, March.

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