Free Access
Issue
ESAIM: PS
Volume 5, 2001
Page(s) 1 - 31
DOI https://doi.org/10.1051/ps:2001100
Published online 15 August 2002
  1. A. Barron, L. Birge and P. Massart, Risk bounds for model selection via penalization. Probab. Theory Related Fields 113 (1995) 301-413. [CrossRef] [MathSciNet]
  2. O.V. Besov, V.L. Il'in and S.M. Nikol'skii, Integral representations of functions and imbedding theorems. J. Wiley, New York (1978).
  3. L. Birge and P. Massart, From model selection to adaptive estimation, Festschrift fur Lucien Le Cam. Springer (1997) 55-87.
  4. L.D. Brown and M.G. Low, A constrained risk inequality with application to nonparametric functional estimation. Ann. Statist. 24 (1996) 2524-2535. [CrossRef] [MathSciNet]
  5. C. Butucea, The adaptive rates of convergence in a problem of pointwise density estimation. Statist. Probab. Lett. 47 (2000) 85-90. [CrossRef] [MathSciNet]
  6. C. Butucea, Numerical results concerning a sharp adaptive density estimator. Comput. Statist. 1 (2001).
  7. L. Devroye and G. Lugosi, A universally acceptable smoothing factor for kernel density estimates. Ann. Statist. 24 (1996) 2499-2512. [CrossRef] [MathSciNet]
  8. D.L. Donoho, I. Johnstone, G. Kerkyacharian and D. Picard, Wavelet shrinkage: Asymptopia? J. R. Stat. Soc. Ser. B Stat. Methodol. 57 (1995) 301-369.
  9. D.L. Donoho, I. Johnstone, G. Kerkyacharian and D. Picard, Density estimation by wavelet thresholding. Ann. Statist. 24 (1996) 508-539. [CrossRef] [MathSciNet]
  10. D.L. Donoho and M.G. Low, Renormalization exponents and optimal pointwise rates of convergence. Ann. Statist. 20 (1992) 944-970. [CrossRef] [MathSciNet]
  11. S.Yu. Efromovich, Nonparametric estimation of a density with unknown smoothness. Theory Probab. Appl. 30 (1985) 557-568. [CrossRef]
  12. S.Yu. Efromovich and M.S. Pinsker, An adaptive algorithm of nonparametric filtering. Automat. Remote Control 11 (1984) 1434-1440.
  13. A. Goldenshluger and A. Nemirovski, On spatially adaptive estimation of nonparametric regression. Math. Methods Statist. 6 (1997) 135-170. [MathSciNet]
  14. G.K. Golubev, Adaptive asymptotically minimax estimates of smooth signals. Problems Inform. Transmission 23 (1987) 57-67.
  15. G.K. Golubev, Quasilinear estimates for signals in Formula . Problems Inform. Transmission 26 (1990) 15-20. [MathSciNet]
  16. G.K. Golubev, Nonparametric estimation of smooth probability densities in Formula . Problems Inform. Transmission 28 (1992) 44-54. [MathSciNet]
  17. G.K. Golubev and M. Nussbaum, Adaptive spline estimates in a nonparametric regression model. Theory Probab. Appl. 37 (1992) 521-529. [CrossRef] [MathSciNet]
  18. I.A. Ibragimov and R.Z. Hasminskii, Statistical estimation: Asymptotic theory. Springer-Verlag, New York (1981).
  19. A. Juditsky, Wavelet estimators: Adapting to unknown smoothness. Math. Methods Statist. 6 (1997) 1-25. [MathSciNet]
  20. G. Kerkyacharian and D. Picard, Density estimation by kernel and wavelet method, optimality in Besov space. Statist. Probab. Lett. 18 (1993) 327-336. [CrossRef] [MathSciNet] [PubMed]
  21. G. Kerkyacharian, D. Picard and K. Tribouley, Formula adaptive density estimation. Bernoulli 2 (1996) 229-247. [MathSciNet]
  22. J. Klemelä and A.B. Tsybakov, Sharp adaptive estimation of linear functionals, Prépublication 540. LPMA Paris 6 (1999).
  23. O.V. Lepskii, On a problem of adaptive estimation in Gaussian white noise. Theory Probab. Appl. 35 (1990) 454-466. [CrossRef] [MathSciNet]
  24. O.V. Lepskii, Asymptotically minimax adaptive estimation I: Upper bounds. Optimally adaptive estimates. Theory Probab. Appl. 36 (1991) 682-697. [CrossRef]
  25. O.V. Lepskii, On problems of adaptive estimation in white Gaussian noise. Advances in Soviet Math. Amer. Math. Soc. 12 (1992b) 87-106.
  26. O.V. Lepski and B.Y. Levit, Adaptive minimax estimation of infinitely differentiable functions. Math. Methods Statist. 7 (1998) 123-156. [MathSciNet]
  27. O.V. Lepski, E. Mammen and V.G. Spokoiny, Optimal spatial adaptation to inhomogeneous smoothness: An approach based on kernel estimates with variable bandwidth selectors. Ann. Statist. 25 (1997) 929-947. [CrossRef] [MathSciNet]
  28. O.V. Lepski and V.G. Spokoiny, Optimal pointwise adaptive methods in nonparametric estimation. Ann. Statist. 25 (1997) 2512-2546. [CrossRef] [MathSciNet]
  29. D. Pollard, Convergence of Stochastic Processes. Springer-Verlag, New York (1984).
  30. A.B. Tsybakov, Pointwise and sup-norm sharp adaptive estimation of functions on the Sobolev classes. Ann. Statist. 26 (1998) 2420-2469. [CrossRef] [MathSciNet]
  31. S. Van de Geer, A maximal inequality for empirical processes, Technical Report TW 9505. University of Leiden, Leiden (1995).

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.