Robust kernels for kernel density estimation

Abstract

The likelihood cross validation (LCV) and the least square cross validation (LSCV) are two commonly used methods of bandwidth selection in kernel density estimation. The LCV is generally more efficient but sensitive to tail-heaviness; in contrast, the LSCV fares well for heavy-tailed distributions but tends to undersmooth and is generally more variable. In this study, we propose two novel kernel functions that are robust against heavy-tailed distributions and at the same time adaptive with respect to the sample tail-heaviness in a data-driven manner. The proposed method is simple to implement. Our simulations show that it performs similarly to the LCV for regular- and thin-tailed distributions and outperforms the LSCV for heavy-tailed distributions, suggesting that it can be an overall competitive alternative. An empirical application to income distribution estimation is provided.