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Nonparametric estimation of density under bias and multiplicative censoring via wavelet methods

  • Abbaszadeh, Mohammad
  • Chesneau, Christophe
  • Doosti, Hassan
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    The density estimation problem under bias and multiplicative censoring is considered. Adopting the wavelet approach, we construct a linear nonadaptive estimator and a nonlinear adaptive estimator. The adaptive one belongs to the family of the hard thresholding estimators. We evaluate their performances by determining upper bounds of the mean integrated squared error over a wide range of functions. Sharp upper bounds are obtained.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212000260
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    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 5 ()
    Pages: 932-941

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:5:p:932-941
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    1. Iain M. Johnstone & GĂ©rard Kerkyacharian & Dominique Picard & Marc Raimondo, 2004. "Wavelet deconvolution in a periodic setting," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 547-573.
    2. E. Brunel & F. Comte & A. Guilloux, 2009. "Nonparametric density estimation in presence of bias and censoring," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 18(1), pages 166-194, May.
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