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Adaptive Density Estimation in Deconvolution Problems with Unknown Error Distribution

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Author Info

  • Johanna Kappus

    ()
    (Intitut für Mathematik-Universität Rostock)

  • Gwennaelle Mabon

    ()
    (CREST and Université Paris-Descartes)

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    Abstract

    A density deconvolution problem with unknown distribution of the errors is considered. To make the target density identifiable, one has to assume that some additional information on the noise is available. We consider two different models: the framework where some additional sample of the pure noise is available, as well as the repeated observation model, where the contaminated random variable of interest can be observed repeatedly. We introduce kernel estimators and present upper risk bounds. The focus of this work lies on the optimal data driven choice of the smoothing parameter using a penalization strategy

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    Bibliographic Info

    Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2013-31.

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    Length: 23
    Date of creation: Dec 2013
    Date of revision:
    Handle: RePEc:crs:wpaper:2013-31

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    Related research

    Keywords: Adaptive estimation. Deconvolution. Density estimation. Mean square risk. Nonparametric methods. Replicate observations;

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    1. Neumann, Michael H., 2007. "Deconvolution from panel data with unknown error distribution," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1955-1968, November.
    2. Stéphane Bonhomme & Jean-Marc Robin, 2010. "Generalized Non-Parametric Deconvolution with an Application to Earnings Dynamics," Review of Economic Studies, Oxford University Press, vol. 77(2), pages 491-533.
    3. A. Delaigle & I. Gijbels, 2004. "Bootstrap bandwidth selection in kernel density estimation from a contaminated sample," Annals of the Institute of Statistical Mathematics, Springer, vol. 56(1), pages 19-47, March.
    4. F. Comte & C. Lacour, 2011. "Data‐driven density estimation in the presence of additive noise with unknown distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(4), pages 601-627, 09.
    5. Li, Tong & Vuong, Quang, 1998. "Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 139-165, May.
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