Empirical likelihood confidence intervals for nonparametric density estimation

We suggest using empirical likelihood in conjunction with the kernel method to construct confidence intervals for the value of a probability density f at a point x. This suggestion arises from a simulation study which shows that confidence intervals produced by the kernel-based percentle-t bootstrap do not have the coverage claimed by the theory. This coverage discrepancy is due to a conflict between the prescribed undersmoothing and the explicit variance estimate needed by the percentile-t method. Empirical likelihood avoids this conflict by studentising internally. We show that the empirical likelihood produces confidence intervals having theoretical coverage accuracy of the same order of magnitude as the bootstrap, and which are also empirically more accurate.