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

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  • Abbaszadeh, Mohammad
  • Chesneau, Christophe
  • Doosti, Hassan

Abstract

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.

Suggested Citation

  • Abbaszadeh, Mohammad & Chesneau, Christophe & Doosti, Hassan, 2012. "Nonparametric estimation of density under bias and multiplicative censoring via wavelet methods," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 932-941.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:5:p:932-941
    DOI: 10.1016/j.spl.2012.01.016
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    References listed on IDEAS

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    1. 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;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 166-194, May.
    2. A. Antoniadis, 1997. "Wavelets in statistics: A review," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 6(2), pages 97-130, August.
    3. Iain M. Johnstone & Gérard 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, August.
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    Cited by:

    1. R. Zamini & V. Fakoor & M. Sarmad, 2015. "On estimation of a density function in multiplicative censoring," Statistical Papers, Springer, vol. 56(3), pages 661-676, August.
    2. Chesneau, Christophe & Dewan, Isha & Doosti, Hassan, 2016. "Nonparametric estimation of a quantile density function by wavelet methods," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 161-174.
    3. Elodie Brunel & Fabienne Comte & Valentine Genon-Catalot, 2016. "Nonparametric density and survival function estimation in the multiplicative censoring model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 570-590, September.

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