A comparative review of bandwidth selection for kernel density estimation

In kernel density estimation, a crucial step is to select a proper smoothing parameter (bandwidth). The bandwidth considerably affects the appearance of the density estimate. The most studied procedure is cross-validation. It is well known that cross-validation is subject to large sample variation and often selects smaller bandwidth. Recently, some procedures have been proposed to remedy the difficulties. The implementation, the asymptotic properties and the empirical performance of several bandwidth selectors are investigated. Based on the sample characteristic function, it is shown that these bandwidth selectors have a similar form. The main difference is in the selection of a second bandwidth to estimate the mean integrated squared errors. Our simulation study indicates that the selection of the second bandwidth greatly affects the performance of the procedures.