Computing confidence intervals for log-concave densities

In Balabdaoui, Rufibach, and Wellner (2009), pointwise asymptotic theory was developed for the nonparametric maximum likelihood estimator of a log-concave density. Here, the practical aspects of their results are explored. Namely, the theory is used to develop pointwise confidence intervals for the true log-concave density. To do this, the quantiles of the limiting process are estimated and various ways of estimating the nuisance parameter appearing in the limit are studied. The finite sample size behavior of these estimated confidence intervals is then studied via a simulation study of the empirical coverage probabilities.