Bootstrap Bias Correction for Improved Coverage Accuracy in Nonparametric Inference

Abstract

Nonparametric inference under MSE-optimal bandwidths requires correcting for non-negligible bias. We propose a bootstrap procedure that incorporates robust bias correction into the resampling step, delivering valid confidence intervals without undersmoothing. We show the method achieves correct coverage uniformly over a class of data-generating processes and derive its higher-order properties relative to the analytical approach of Calonico et al. (2018). Simulations reveal that the bootstrap analogue matches or improves upon asymptotic intervals in finite samples, particularly in the tails of the density where bias is most severe.

Keywords: Edgeworth expansion; Kernel methods, Density estimation

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