Title: Adaptive Clustering Using Kernel Density Estimators,
Abstract: We investigate statistical properties of a clustering algorithm that receives
level set estimates from a kernel density estimator and then estimates the
first split in the density level cluster tree if such a split is present or
detects the absence of such a split. Key aspects of our analysis include finite
sample guarantees, consistency, rates of convergence, and an adaptive
data-driven strategy for chosing the kernel bandwidth. For the rates and the
adaptivity we do not need continuity assumptions on the density such as
Hölder continuity, but only require intuitive geometric assumptions of
non-parametric nature.