On Clustering Procedures and Nonparametric Mixture Estimation

Stéphane Auray, Nicolas Klutchnikoff () and Laurent Rouvière ()
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Nicolas Klutchnikoff: CREST-ENSAI et Université de Strasbourg
Laurent Rouvière: CREST-ENSAI

No 2013-32, Working Papers from Center for Research in Economics and Statistics

Abstract: 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

Keywords: Nonparametric estimation; mixture models; clustering (search for similar items in EconPapers)
Pages: 27
Date: 2013-12
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