A variable bandwidth selector in multivariate kernel density estimation

Based on a random sample of size n from an unknown d-dimensional density f , the problem of selecting the variable (or adaptive) bandwidth in kernel estimation of f is investigated. The common strategy is to express the variable bandwidth at each observation as the product of a local bandwidth factor and a global smoothing parameter. For selecting the local bandwidth factor a method based on cluster analysis is proposed. This method is direct and intuitively appealing. For selecting the global smoothing parameter a method that is an adaptation of the frequency domain approach of selecting the fixed bandwidth in Wu and Tsai (2004) is used. For d = 1 and d = 2, extensive simulation studies have been done to compare the performance of our selector with the selectors of Abramson (1982) and Sain and Scott (1996) and Sain (2002), and the excellent performance of our selector at practical sample sizes is clearly demonstrated.