Using small bias nonparametric density estimators for confidence interval estimation

Marco Di Marzio & Charles C Taylor

Confidence intervals for densities built on the basis of standard nonparametric theory are doomed to have poor coverage rates due to bias. Studies on coverage improvement exist, but reasonably behaved interval estimators are needed. We explore the use of small bias kernel--based methods to construct confidence intervals, in particular using a geometric density estimator that seems particularly suited for this purpose.