Asymptotics for bandwidth selection in nonparametric clustering

In the framework of nonparametric clustering, clusters are defined as the domains of attraction of the modes of the density function assumed to underlie the data. To identify clusters, an estimate of the density is then needed, with kernel density estimator taking the lion’s share. When resorting to these methods a fine tuning of the amount of smoothing, governing the modal structure of the density, is required. While thoroughly analyzed in the context of density estimation, this issue has been scarcely studied for clustering purposes. In this work the problem is addressed from an asymptotic perspective. A sensible distance among groupings is introduced and its asymptotic expression is derived and exploited in order to obtain a bandwidth selection procedure specifically tailored for nonparametric clustering