Quantile estimation for discrete data via empirical likelihood

Jien Chen and Nicole Lazar

Journal of Nonparametric Statistics, 2010, vol. 22, issue 2, 237-255

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.

Date: 2010
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Citations: View citations in EconPapers (2)

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DOI: 10.1080/10485250903301525

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