Edgeworth expansions for nonparametric density estimators, with applications

We develop Edgeworth expansions for kernel density estimators, and for their bootstrap counterparts. Those results are applied to the bootstrap confidence interval problem for densities, paying particular attention to the issue of bias. Two approaches to bias correction are considered: explicit bias estimation, and deliberate undersmoothing to render bias negligible, The latter method is shown to have advantages over the former from the viewpoint of coverage accuracy of onesided confidence intervals. Addition-ally, it produces shorter two-sided intervals Keywords: Bootstrapconfidence intervalcoverage errordensity functionEdgeworth expansion