A Comparison of Higher-Order Bias Kernel Density Estimators

Abstract

We consider many kernel-based density estimators, all theoretically improving bias from O ( h 2 ), as the smoothing parameter h → 0, to O ( h 4 ). Examples include higher-order kernels, variable kernel methods, and transformation and multiplicative bias-correction approaches. We stress the similarities between what appear to be disparate approaches. In particular, we show how the mean squared errors of all methods have the same form. Our main practical contribution is a comparative simulation study that isolates the most promising approaches. It remains debatable, however, as to whether even the best methods give worthwhile improvements, at least for small-to-moderate sample exploratory purposes.