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.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty