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New Model‐assisted Estimators for the Distribution Function Using the Pseudo Empirical Likelihood Method

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  • M. Rueda
  • J.F. Muñoz

Abstract

This paper proposes using a model‐assisted approach based on the pseudo empirical likelihood method to construct estimators for the finite population distribution function. It shows that the proposed sample‐based estimators are genuine distribution functions that exhibit several attractive features, such as the fact that they do not depend on unknown parameters, and good performance at any argument is expected to be obtained. Consequently, estimation of other measures, such as quantiles, is a problem that is efficiently addressed by the proposed methodology and applications in various areas are therefore derived. Simulation studies based upon real and artificial populations show that the proposed estimators perform better than the existing ones. A practical situation in which the proposed estimators can be applied is also described.

Suggested Citation

  • M. Rueda & J.F. Muñoz, 2009. "New Model‐assisted Estimators for the Distribution Function Using the Pseudo Empirical Likelihood Method," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 63(2), pages 227-244, May.
    • Handle: RePEc:bla:stanee:v:63:y:2009:i:2:p:227-244
    DOI: 10.1111/j.1467-9574.2009.00421.x
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    References listed on IDEAS

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    1. J. Chen, 2002. "Using empirical likelihood methods to obtain range restricted weights in regression estimators for surveys," Biometrika, Biometrika Trust, vol. 89(1), pages 230-237, March.
    2. Changbao Wu, 2003. "Optimal calibration estimators in survey sampling," Biometrika, Biometrika Trust, vol. 90(4), pages 937-951, December.
    3. M. Rueda & J. Muñoz & Y. Berger & A. Arcos & S. Martínez, 2007. "Pseudo empirical likelihood method in the presence of missing data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 65(3), pages 349-367, May.
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    1. Martínez, S. & Rueda, M. & Arcos, A. & Martínez, H. & Sánchez-Borrego, I., 2011. "Post-stratified calibration method for estimating quantiles," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 838-851, January.
    2. Muñoz, J.F. & Arcos, A. & Álvarez, E. & Rueda, M., 2014. "New ratio and difference estimators of the finite population distribution function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 102(C), pages 51-61.

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