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On Clustering Procedures and Nonparametric Mixture Estimation


  • Stéphane Auray

    () (CREST-ENSAI)

  • Nicolas Klutchnikoff

    () (CREST-ENSAI et Université de Strasbourg)

  • Laurent Rouvière

    () (CREST-ENSAI)


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

Suggested Citation

  • Stéphane Auray & Nicolas Klutchnikoff & Laurent Rouvière, 2013. "On Clustering Procedures and Nonparametric Mixture Estimation," Working Papers 2013-32, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2013-32

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    References listed on IDEAS

    1. C. A. Glasbey & K. V. Mardia, 2001. "A penalized likelihood approach to image warping," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 465-492.
    2. Horowitz, Joel L & Spokoiny, Vladimir G, 2001. "An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model against a Nonparametric Alternative," Econometrica, Econometric Society, vol. 69(3), pages 599-631, May.
    3. Jianqing Fan & Jiancheng Jiang, 2007. "Nonparametric inference with generalized likelihood ratio tests," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(3), pages 409-444, December.
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