IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v82y2012i5p932-941.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212000260
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2012.01.016?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Emmanouil Androulakis & Christos Koukouvinos & Kalliopi Mylona & Filia Vonta, 2010. "A real survival analysis application via variable selection methods for Cox's proportional hazards model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(8), pages 1399-1406.
    2. Bissantz, Nicolai & Holzmann, Hajo, 2007. "Statistical inference for inverse problems," Technical Reports 2007,40, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    3. E. Androulakis & C. Koukouvinos, 2013. "A new variable selection method for uniform designs," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(12), pages 2564-2578, December.
    4. Jérémie Bigot & Sébastien Van Bellegem, 2009. "Log‐density Deconvolution by Wavelet Thresholding," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 749-763, December.
    5. A. Karagrigoriou & C. Koukouvinos & K. Mylona, 2010. "On the advantages of the non-concave penalized likelihood model selection method with minimum prediction errors in large-scale medical studies," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(1), pages 13-24.
    6. Chesneau, Christophe, 2007. "Regression with random design: A minimax study," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 40-53, January.
    7. Xingwei Tong & Xin He & Liuquan Sun & Jianguo Sun, 2009. "Variable Selection for Panel Count Data via Non‐Concave Penalized Estimating Function," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 620-635, December.
    8. Raimondo, Marc & Stewart, Michael, 2007. "The WaveD Transform in R: Performs Fast Translation-Invariant Wavelet Deconvolution," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 21(i02).
    9. Ertefaie Ashkan & Asgharian Masoud & Stephens David A., 2018. "Variable Selection in Causal Inference using a Simultaneous Penalization Method," Journal of Causal Inference, De Gruyter, vol. 6(1), pages 1-16, March.
    10. Christophe Chesneau & Fabien Navarro, 2017. "On the pointwise mean squared error of a multidimensional term-by-term thresholding wavelet estimator," Working Papers 2017-68, Center for Research in Economics and Statistics.
    11. Felix Abramovich & Claudia Angelini & Daniela Canditiis, 2007. "Pointwise optimality of Bayesian wavelet estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(3), pages 425-434, September.
    12. Birke, Melanie & Bissantz, Nicolai, 2007. "Shape constrained estimators in inverse regression models with convolution-type operator," Technical Reports 2007,35, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    13. Benhaddou, Rida, 2017. "On minimax convergence rates under Lp-risk for the anisotropic functional deconvolution model," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 120-125.
    14. Liu-Cang Wu & Zhong-Zhan Zhang & Deng-Ke Xu, 2012. "Variable selection in joint mean and variance models of Box--Cox transformation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(12), pages 2543-2555, August.
    15. Yao Dong & He Jiang, 2018. "A Two-Stage Regularization Method for Variable Selection and Forecasting in High-Order Interaction Model," Complexity, Hindawi, vol. 2018, pages 1-12, November.
    16. Christophe Chesneau, 2014. "A Note on Wavelet Estimation of the Derivatives of a Regression Function in a Random Design Setting," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-8, April.
    17. Bissantz, Nicolai & Hohage, T. & Munk, Axel & Ruymgaart, F., 2007. "Convergence rates of general regularization methods for statistical inverse problems and applications," Technical Reports 2007,04, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    18. Abramovich, Felix & Besbeas, Panagiotis & Sapatinas, Theofanis, 2002. "Empirical Bayes approach to block wavelet function estimation," Computational Statistics & Data Analysis, Elsevier, vol. 39(4), pages 435-451, June.
    19. Zhang, Jing & Wang, Qin & Mays, D'Arcy, 2021. "Robust MAVE through nonconvex penalized regression," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    20. Gao, Yan & Zhang, Xinyu & Wang, Shouyang & Zou, Guohua, 2016. "Model averaging based on leave-subject-out cross-validation," Journal of Econometrics, Elsevier, vol. 192(1), pages 139-151.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:82:y:2012:i:5:p:932-941. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.