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Estimation of more than one parameters in stratified sampling with fixed budget

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  • Rahul Varshney
  • Najmussehar
  • M. Ahsan

Abstract

In a multivariate stratified sampling more than one characteristic are defined on every unit of the population. An optimum allocation which is optimum for one characteristic will generally be far from optimum for others. A compromise criterion is needed to work out a usable allocation which is optimum, in some sense, for all the characteristics. When auxiliary information is also available the precision of the estimates of the parameters can be increased by using it. Furthermore, if the travel cost within the strata to approach the units selected in the sample is significant the cost function remains no more linear. In this paper an attempt has been made to obtain a compromise allocation based on minimization of individual coefficients of variation of the estimates of various characteristics, using auxiliary information and a nonlinear cost function with fixed budget. A new compromise criterion is suggested. The problem is formulated as a multiobjective all integer nonlinear programming problem. A solution procedure is also developed using goal programming technique. Copyright Springer-Verlag 2012

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:75:y:2012:i:2:p:185-197
    DOI: 10.1007/s00186-012-0380-y
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    References listed on IDEAS

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    1. 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.
    2. M. Ahsan & S. Khan, 1982. "Optimum allocation in multivariate stratified random sampling with overhead cost," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 29(1), pages 71-78, December.
    3. 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. 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.
    2. Yousaf Shad Muhammad & Ijaz Hussain & Alaa Mohamd Shoukry, 2016. "Multivariate Multi-Objective Allocation in Stratified Random Sampling: A Game Theoretic Approach," PLOS ONE, Public Library of Science, vol. 11(12), pages 1-11, December.

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    2. 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.

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