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An exact algorithm for the stratification problem with proportional allocation

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Abstract

We report a new optimal resolution for the statistical stratification problem under proportional sampling allocation among strata. Consider a finite population of N units, a random sample of n units selected from this population and a number L of strata. Thus, we have to define which units belong to each stratum so as to minimize the variance of a total estimator for one desired variable of interest in each stratum, and consequently reduce the overall variance for such quantity. In order to solve this problem, an optimal algorithm based on the concept of minimal path in a graph is proposed and assessed. Computational results using real data from IBGE (Brazilian Central Statistical Office) are provided.

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References

  1. Ahuja K.R., Magnanti O., Orlin J.B.: Networks Flows: Theory, Algorithms and Applications. A Simon & Schuster Company, Prentice Hall (1993)

    Google Scholar 

  2. Chen, S., Nahrstedt, K.: On finding multi-constrained paths. In: Proc. of IEEE International Conference on Communications, Atlanta, pp. 874–879 (1998)

  3. Cochran W.G.: Sampling Techniques, 3rd edn. Wiley, New York (1977)

    MATH  Google Scholar 

  4. Dalenius T., Hodges J.L. Jr: Minimum variance stratification. Skandinavisk Aktuarietidskrift 54, 88–101 (1959)

    MATH  Google Scholar 

  5. Gunning P., Horgan J.M.: A new algorithm for the construction of stratum boundaries in skewed populations. Surv. Methodol. 30, 159–166 (2004)

    Google Scholar 

  6. Hedlin D.A.: A procedure for stratification by an extended ekman rule. J. Official Stat. 16, 15–29 (2000)

    Google Scholar 

  7. Kozak M.: Optimal stratification using random search method in agricultural surveys. Stat. Trans. 6, 797–806 (2004)

    Google Scholar 

  8. Lavallée P., Hidiroglou M.A.: On the stratification of skewed populations. Surv. Methodol. (Stat. Canada) 14, 33–43 (1988)

    Google Scholar 

  9. Rivest L.P.: A generalization of the Lavallée and Hidiroglou Algorithm for stratification in business surveys. Surv. Methodol. (Stat. Canada) 28, 191–198 (2002)

    Google Scholar 

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Authors and Affiliations

  1. IBGE, Brazilian Central Statistical Office, Rio de Janeiro, 20031-170, Brazil

    José Brito, Maurício Lila & Flávio Montenegro

  2. COPPE, Systems Engineering, Federal University of Rio de Janeiro, P.O. Box 68511, Rio de Janeiro, 21941-972, Brazil

    Nelson Maculan

Authors
  1. José Brito
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  2. Nelson Maculan
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  3. Maurício Lila
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  4. Flávio Montenegro
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Correspondence to José Brito.

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Brito, J., Maculan, N., Lila, M. et al. An exact algorithm for the stratification problem with proportional allocation. Optim Lett 4, 185–195 (2010). https://doi.org/10.1007/s11590-009-0157-2

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  • DOI: https://doi.org/10.1007/s11590-009-0157-2

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