Quantile estimation for discrete data via empirical likelihood

Jien Chen, Nicole A. Lazar

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)237-255
Number of pages19
JournalJournal of Nonparametric Statistics
Volume22
Issue number2
DOIs
StatePublished - Feb 2010

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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