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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 260573, 7 pages
http://dx.doi.org/10.1155/2013/260573
Research Article

Wavelet Optimal Estimations for Density Functions under Severely Ill-Posed Noises

Department of Applied Mathematics, Beijing University of Technology, Pingle Yuan 100, Beijing 100124, China

Received 6 October 2013; Accepted 13 November 2013

Academic Editor: Ding-Xuan Zhou

Copyright © 2013 Rui Li and Youming Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Pensky and B. Vidakovic, “Adaptive wavelet estimator for nonparametric density deconvolution,” The Annals of Statistics, vol. 27, no. 6, pp. 2033–2053, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. J. Fan and J.-Y. Koo, “Wavelet deconvolution,” IEEE Transactions on Information Theory, vol. 48, no. 3, pp. 734–747, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. K. Lounici and R. Nickl, “Global uniform risk bounds for wavelet deconvolution estimators,” The Annals of Statistics, vol. 39, no. 1, pp. 201–231, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. R. Li and Y. Liu, “Wavelet optimal estimations for a density with some additive noises,” Applied and Computational Harmonic Analysis, 2013. View at Publisher · View at Google Scholar
  5. I. Daubechies, Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics, Philadelphia, Pa, USA, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  6. W. Hardle, G. Kerkyacharian, D. Picard, and A. Tsybakov, Wavelets, Approximation and Statistical Applications, Springer, New York, NY, USA, 1997.
  7. A. B. Tsybakov, Introduction to Nonparametric Estimation, Springer, Berlin, Germany, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  8. R. DeVore, G. Kerkyacharian, D. Picard, and V. Temlyakov, “Approximation methods for supervised learning,” Foundations of Computational Mathematics, vol. 6, no. 1, pp. 3–58, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet