Abstract

Kernel density estimation (KDE) is a widely used nonparametric tool for recovering unknown probability density functions without strong distributional assumptions. However, even well-tuned kernel density estimators often exhibit non-negligible bias, which can potentially affect the accuracy of subsequent statistical inference. In this paper, we adapt the bias-reduction approach of Cheng et al. (2018), originally proposed for kernel regression, to the classical kernel density estimator. The resulting method reduces the order of magnitude of the asymptotic bias while maintaining the variance at the same order as that of the standard estimator. Unlike traditional bias-reduction strategies based on higher-order kernels or variable kernels, our approach has a simple computational structure and does not require oscillatory kernel functions or pilot estimates for local bandwidths. We derive the theoretical properties of the proposed estimator and assess its performance through simulation studies and two real-data applications. The results show that the bias-reduced estimator often achieves lower mean integrated squared errors than the standard KDE, particularly for finite samples and high-curvature target densities.

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