On Clustering Procedures and Nonparametric Mixture Estimation

This paper deals with nonparametric estimation of conditional densities in mixture models. The proposed approach consists to perform a preliminary clustering algorithm to guess the mixture component of each observation. Conditional densities of the mixture model are then estimated using kernel density estimates applied separately to each cluster. We investigate the expected L1-error of the resulting estimates with regards to the performance of the clustering algorithm. In particular, we prove that these estimates achieve optimal rates over classical nonparametric density classes under mild assumptions on the clustering method used. Finally, we offer examples of clustering algorithms verifying the required assumptions