Free Access
Issue
ESAIM: PS
Volume 12, April 2008
Page(s) 327 - 344
DOI https://doi.org/10.1051/ps:2007038
Published online 08 May 2008
  1. L.D. Brown, T. Cai, M.G. Low and C. Zang, Asymptotic equivalence theory for nonparametric regression with random design. Ann. Stat. 24 (2002) 2399–2430. [Google Scholar]
  2. C. Butucea, Deconvolution of supersmooth densities with smooth noise. Canad. J. Statist. 32 (2004) 181–192. [CrossRef] [MathSciNet] [Google Scholar]
  3. C. Butucea and A.B. Tsybakov, Sharp optimality for density deconvolution with dominating bias. (2004), arXiv:math.ST/0409471. [Google Scholar]
  4. L. Cavalier, G.K. Golubev, O.V. Lepski and A.B. Tsybakov, Block thresholding and sharp adaptive estimation in severely ill-posed problems. Theory Probab. Appl. 48 (2003) 534–556. [Google Scholar]
  5. G.K. Golubev and R.Z. Khasminskii, Statistical approach to Cauchy problem for Laplace equation. State of the Art in Probability and Statistics, Festschrift for W.R. van, Zwet M. de Gunst, C. Klaassen and van der Vaart Eds., IMS Lecture Notes Monograph Series 36 (2001) 419–433. [Google Scholar]
  6. R.J. Carrol and P. Hall, Optimal rates of convergence for deconvolving a density J. Amer. Statist. Assoc. 83 (1988) 1184–1186. [Google Scholar]
  7. D.L. Donoho, Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition. Appl. Comput. Harmon. Anal. 2 (1992) 101–126. [CrossRef] [MathSciNet] [Google Scholar]
  8. S. Efroimovich, Nonparametric Curve Estimation: Methods, Theory and Applications. New York, Springer (1999). [Google Scholar]
  9. S. Efromovich and M. Pinsker, Sharp optimal and adaptive estimation for heteroscedastic nonparametric regression. Statistica Cinica 6 (1996) 925–942. [Google Scholar]
  10. M.S. Ermakov, Minimax estimation in a deconvolution problem. J. Phys. A: Math. Gen. 25 (1992) 1273–1282. [CrossRef] [Google Scholar]
  11. M.S. Ermakov, Asymptotically minimax and Bayes estimation in a deconvolution problem. Inverse Problems 19 (2003) 1339–1359. [CrossRef] [MathSciNet] [Google Scholar]
  12. J. Fan, Asymptotic normality for deconvolution kernel estimators. Sankhia Ser. A 53 (1991) 97–110. [Google Scholar]
  13. J. Fan, On the optimal rates of convergence for nonparametric deconvolution problems. Ann. Statist. 19 (1991) 1257–1272. [CrossRef] [MathSciNet] [Google Scholar]
  14. A. Goldenshluger, On pointwise adaptive nonparametric deconvolution. Bernoulli 5 (1999) 907–25. [CrossRef] [MathSciNet] [Google Scholar]
  15. Yu K. Golubev, B.Y. Levit and A.B. Tsybakov, Asymptotically efficient estimation of Analitic functions in Gaussian noise. Bernoulli 2 (1996) 167–181. [CrossRef] [MathSciNet] [Google Scholar]
  16. I.A. Ibragimov and R.Z. Hasminskii, Estimation of distribution density belonging to a class of entire functions. Theory Probab. Appl. 27 (1982) 551–562. [CrossRef] [Google Scholar]
  17. P.A. Jansson, Deconvolution, with application to Spectroscopy. New York, Academic (1984). [Google Scholar]
  18. I.M. Johnstone, G. Kerkyacharian, D. Picard and M.Raimondo, Wavelet deconvolution in a periodic setting. J. Roy. Stat. Soc. Ser B. 66 (2004) 547–573. [CrossRef] [Google Scholar]
  19. I.M. Johnstone and M. Raimondo, Periodic boxcar deconvolution and Diophantine approximation. Ann. Statist. 32 (2004) 1781–1805. [CrossRef] [MathSciNet] [Google Scholar]
  20. J. Kalifa and S. Mallat, Threshholding estimators for linear inverse problems and deconvolutions. Ann. Stat. 31 (2003) 58–109. [CrossRef] [MathSciNet] [Google Scholar]
  21. S. Kassam and H. Poor, Robust techniques for signal processing. A survey. Proc. IEEE 73 (1985) 433–481. [CrossRef] [Google Scholar]
  22. M.R. Leadbetter, G. Lindgren and H. Rootzen, Extremes and Related Properties of Random sequences and Processes. Springer-Verlag NY (1986). [Google Scholar]
  23. R. Neelamani, H. Choi, R.G. Baraniuk, ForWaRD: Fourier-wavelet regularized deconvolution for ill-conditioned systems. IEEE Trans. Signal Process. 52 (2004) 418–433. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  24. M. Nussbaum, Asymptotic equivalence of density estimation and Gaussian white noise. Ann. Stat. 24 (1996) 2399–2430. [CrossRef] [MathSciNet] [Google Scholar]
  25. M. Pensky and B. Vidakovic, Adaptive wavelet estimator for nonparametric density deconvolution. Ann. Statist. 27 (1999) 2033–2053. [CrossRef] [MathSciNet] [Google Scholar]
  26. M.S. Pinsker, Optimal filtration of square-integral signal in Gaussian noise. Problems Inform. Transm. 16 (1980) 52–68. [Google Scholar]
  27. M. Schipper, Optimal rates and constants in L2-minimax estimation of probability density functions. Math. Methods Stat. 5 (1996) 253–274. [Google Scholar]
  28. A.J. Smola, B. Scholkopf and K. Miller, The connection between regularization operators and support vector kernels. Newral Networks 11 (1998) 637–649. [CrossRef] [Google Scholar]
  29. A. Tikhonov and V. Arsenin, Solution of Ill-Posed Problems. New-York, Wiley (1977). [Google Scholar]
  30. A.B. Tsybakov, On the best rate of adaptive estimation in some inverse problems. C.R. Acad. Sci. Paris, Serie 1 330 (2000) 835–840. [Google Scholar]
  31. N. Wiener, Extrapolation, Interpolation and Smoothing of Stationary Time Series. New York, Wiley (1950). [Google Scholar]
  32. * This paper was partially supported by RFFI Grants 02-01-00262, 4422.2006.1. [Google Scholar]

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