Bandwidth selection for kernel density estimation of fat-tailed and skewed distributions

Abstract

Applied researchers using kernel density estimation have worked with optimal bandwidth rules that invariably assumed that the reference density is Normal (optimal only if the true underlying density is Normal). We offer four new optimal bandwidth rules-of-thumb based on other infinitely supported distributions: Logistic, Laplace, Student's t and Asymmetric Laplace. Additionally, we propose a psuedo rule-of-thumb (ROT) bandwidth based on a Gram-Charlier expansion of the unknown reference density that is linked to the empirical skewness and kurtosis of the data. The intellectual investment needed to implement these new optimal bandwidths is practically zero. We discuss the behaviour of these bandwidths as it links to differences in skewness and kurtosis to the Normal reference ROT. We further propose model selection criteria for bandwidth choice when the true underlying density is unknown. The performance of these new ROT bandwidths are assessed in a variety of Monte Carlo simulations as well as in two empirical illustrations, the well known data set of annual snowfall in Buffalo, New York, and a timely example on stock market trading.