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Optimum multivariate stratified double sampling design: Chebyshev's Goal Programming approach

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  • Shazia Ghufran
  • Saman Khowaja
  • M.J. Ahsan

Abstract

In stratified sampling when strata weights are unknown a double sampling technique may be used to estimate them. A large simple random sample from the unstratified population is drawn and units falling in each stratum are recorded. A stratified random sample is then selected and simple random subsamples are obtained out of the previously selected units of the strata. This procedure is called double sampling for stratification. If the problem of non-response is there, then subsamples are divided into classes of respondents and non-respondents. A second subsample is then obtained out of the non-respondents and an attempt is made to obtain the information by increasing efforts, persuasion and call backs. In this paper, the problem of obtaining a compromise allocation in multivariate stratified random sampling is discussed when strata weights are unknown and non-response is present. The problem turns out to be a multiobjective non-linear integer programming problem. An approximation of the problem to an integer linear programming problem by linearizing the non-linear objective functions at their individual optima is worked out. Chebyshev's goal programming technique is then used to solve the approximated problem. A numerical example is also presented to exhibit the practical application of the developed procedure.

Suggested Citation

  • Shazia Ghufran & Saman Khowaja & M.J. Ahsan, 2015. "Optimum multivariate stratified double sampling design: Chebyshev's Goal Programming approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(5), pages 1032-1042, May.
    • Handle: RePEc:taf:japsta:v:42:y:2015:i:5:p:1032-1042
    DOI: 10.1080/02664763.2014.995603
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    References listed on IDEAS

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    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. M. G. M. Khan & M. J. Ahsan & Nujhat Jahan, 1997. "Compromise allocation in multivariate stratified sampling: An integer solution," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(1), pages 69-79, February.
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    Cited by:

    1. Carlin C. F. Chu & Simon S. W. Li, 2024. "A multiobjective optimization approach for threshold determination in extreme value analysis for financial time series," Computational Management Science, Springer, vol. 21(1), pages 1-14, June.
    2. Carlos A. Moreno-Camacho & Jairo R. Montoya-Torres & Anicia Jaegler, 2023. "Sustainable supply chain network design: a study of the Colombian dairy sector," Annals of Operations Research, Springer, vol. 324(1), pages 573-599, May.

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