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Optimum Stratification Using Dynamic Programming with a Mixture of Ratio and Product Estimators under Super Population Model

Author

Listed:
  • Faizan Danish
  • Rafia Jan
  • Muhammad Daniyal
  • Kassim Tawiah

Abstract

In this study, we have utilized two study variables and one auxiliary variable. The auxiliary variable is used as the stratification variable, and we selected the sample using the stratification variable with a mixture of ratio and product estimators. Under super population set‐up, minimal equations have been obtained through minimization of the aggregated variance with the help of the variables under study. The objective function is minimized with respect to the constraints under consideration. The dynamic programming approach has been used to minimize the variance and obtain the optimum strata boundaries. Empirical studies have also been made on the proposed rule utilizing different distributions. A simulation study has been done which shows the gain in precision using the proposed method.

Suggested Citation

  • Faizan Danish & Rafia Jan & Muhammad Daniyal & Kassim Tawiah, 2023. "Optimum Stratification Using Dynamic Programming with a Mixture of Ratio and Product Estimators under Super Population Model," Mathematical Problems in Engineering, John Wiley & Sons, vol. 2023(1).
    • Handle: RePEc:wly:jnlmpe:v:2023:y:2023:i:1:n:3149912
    DOI: 10.1155/2023/3149912
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    References listed on IDEAS

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    1. Karuna Garan Reddy & Mohammad G M Khan & Sabiha Khan, 2018. "Optimum strata boundaries and sample sizes in health surveys using auxiliary variables," PLOS ONE, Public Library of Science, vol. 13(4), pages 1-34, April.
    2. Faizan Danish & S. E. H. Rizvi, 2021. "Approximately optimum strata boundaries for two concomitant stratification variables under proportional allocation," Statistics in Transition New Series, Polish Statistical Association, vol. 22(4), pages 19-40, December.
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