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Optimum design-based ratio estimators of the distribution function

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  • J.F. Mu�oz
  • E. �lvarez
  • M. Rueda

Abstract

The ratio method is commonly used to the estimation of means and totals. This method was extended to the problem of estimating the distribution function. An alternative ratio estimator of the distribution function is defined. A result that compares the variances of the aforementioned ratio estimators is used to define optimum design-based ratio estimators of the distribution function. Different empirical results indicate that the optimum ratio estimators can be more efficient than alternative ratio estimators. In addition, we show by simulations that alternative ratio estimators can have large biases, whereas biases of the optimum ratio estimators are negligible in this situation.

Suggested Citation

  • J.F. Mu�oz & E. �lvarez & M. Rueda, 2014. "Optimum design-based ratio estimators of the distribution function," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(7), pages 1395-1407, July.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:7:p:1395-1407
    DOI: 10.1080/02664763.2013.870983
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    1. Nicholas T. Longford & Maria Grazia Pittau & Roberto Zelli & Riccardo Massari, 2012. "Poverty and inequality in European regions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(7), pages 1557-1576, January.
    2. Sarjinder Singh & Housila Singh & Lakshmi Upadhyaya, 2007. "Chain ratio and regression type estimators for median estimation in survey sampling," Statistical Papers, Springer, vol. 48(1), pages 23-46, January.
    3. Jonathan Haughton & Shahidur R. Khandker, 2009. "Handbook on Poverty and Inequality," World Bank Publications - Books, The World Bank Group, number 11985, December.
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