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Quantile estimation for discrete data via empirical likelihood

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  • Jien Chen
  • Nicole Lazar

Abstract

Quantile estimation for discrete distributions has not been well studied, although discrete data are common in practice. Under the assumption that data are drawn from a discrete distribution, we examine the consistency of the maximum empirical likelihood estimator (MELE) of the pth population quantile θp, with the assistance of a jittering method and results for continuous distributions. The MELE may or may not be consistent for θp, depending on whether or not the underlying distribution has a plateau at the level of p. We propose an empirical likelihood-based categorisation procedure which not only helps in determining the shape of the true distribution at level p but also provides a way of formulating a new estimator that is consistent in any case. Analogous to confidence intervals in the continuous case, the probability of a correct estimate (PCE) accompanies the point estimator. Simulation results show that PCE can be estimated using a simple bootstrap method.

Suggested Citation

  • Jien Chen & Nicole Lazar, 2010. "Quantile estimation for discrete data via empirical likelihood," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(2), pages 237-255.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:2:p:237-255
    DOI: 10.1080/10485250903301525
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    References listed on IDEAS

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    1. Wang Zhou & Bing-Yi Jing, 2003. "Adjusted empirical likelihood method for quantiles," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(4), pages 689-703, December.
    2. Machado, Jose A.F. & Silva, J. M. C. Santos, 2005. "Quantiles for Counts," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1226-1237, December.
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    Cited by:

    1. Jan G. de Gooijer & Ao Yuan, 2011. "Kernel-Smoothed Conditional Quantiles of Correlated Bivariate Discrete Data," Tinbergen Institute Discussion Papers 11-011/4, Tinbergen Institute.
    2. Luke B. Smith & Brian J. Reich & Amy H. Herring & Peter H. Langlois & Montserrat Fuentes, 2015. "Multilevel quantile function modeling with application to birth outcomes," Biometrics, The International Biometric Society, vol. 71(2), pages 508-519, June.

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