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A unified treatment of direct and indirect estimation of a probability density and its derivatives

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  • Abdous, Belkacem
  • Germain, Stéphane
  • Ghazzali, Nadia
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    Abstract

    This paper presents convolution-based estimates of a probability density and its derivatives. The proposed estimates can handle either contaminated data or not and they comprehend some classical estimates such that kernel, regularization estimates. By putting these direct and indirect estimation problems in the same framework, we clearly see how the estimates performances are affected by contamination and by the order of the derivative to be estimated. Minimax optimal rates for the MISE criterion are proposed.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 56 (2002)
    Issue (Month): 3 (February)
    Pages: 239-250

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    Handle: RePEc:eee:stapro:v:56:y:2002:i:3:p:239-250

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    Related research

    Keywords: Kernel estimation Deconvolution Regularization Ill-posed problems Density derivatives Wavelets estimates;

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    1. Ja-Yong Koo, 1999. "Logspline Deconvolution in Besov Space," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 26(1), pages 73-86.
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