Quantile estimation for discrete data via empirical likelihood

Quantile estimation for discrete data via empirical likelihood

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 quanti...

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Bibliographic Details
Published in:Journal of nonparametric statistics 2010-02, Vol.22 (2), p.237-255
Main Authors: Chen, Jien, Lazar, Nicole A.
Format: Article
Language:eng
Subjects:
bootstrap
Bootstrap method
Combinatorics
Confidence intervals
Consistency
discrete distributions
Empirical analysis
empirical likelihood
Estimates
Estimators
jittering
Maximum likelihood method
Nonparametric statistics
quantile estimation
Quantiles
Simulation
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Summary: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 θ p , with the assistance of a jittering method and results for continuous distributions. The MELE may or may not be consistent for θ p , 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.
ISSN:1048-5252
1029-0311