2010/01/28 by Jien Chen, Nicole A. Lazar · 1 citation
Mathematics · Computer Science · #Statistical Methods and Inference #Statistical Methods and Bayesian Inference #Bayesian Methods and Mixture Models
paper · doi:10.1080/10485250903301525
openalex publication_date 2010/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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.