Plug-in bandwidth matrices for bivariate kernel density estimation

Abstract

We consider bandwidth matrix selection for bivariate kernel density estimators. The majority of work in this area has been directed towards selection of diagonal bandwidth matrices, but full bandwidth matrices can give markedly better performance for some types of target density. Our methodological contribution has been to develop a new version of the plug-in selector for full bandwidth matrices. Our approach has the advantage, in comparison to existing full bandwidth matrix plug-in techniques, that it will always produce a finite bandwidth matrix. Furthermore, it requires computation of significantly fewer pilot bandwidths. Numerical studies indicate that the performance of our bandwidth selector is best when implemented with two pilot estimation stages and applied to sphered data. In this case our methodology performs at least as well as any competing method considered, while being simpler to implement than its competitors.