EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 17 (2013) ESAIM: PS, 17 (2013) 472-484 References
Free Access
Issue
ESAIM: PS
Volume 17, 2013
Page(s) 472 - 484
DOI https://doi.org/10.1051/ps/2012002
Published online 03 June 2013
  1. F. Autin, Point de vue maxiset en estimation non paramétrique. Ph.D. thesis, Université Paris 7 (2004). [Google Scholar]
  2. Y. Benyamini and J. Lindenstrauss, Geometric nonlinear functional analysis, Colloquium Publications, vol. 1. American Mathematical Society (AMS) (2000). [Google Scholar]
  3. L. Birgé, Approximation dans les espaces métriques et théorie de l’estimation. Z. Wahrscheinlichkeitstheorie Verw. Gebiete 65 (1983) 181–237. [Google Scholar]
  4. J.P.R. Christensen, On sets of Haar measure zero in Abelian Polish groups. Isr. J. Math. 13 (1972) 255–260. [CrossRef] [Google Scholar]
  5. A. Cohen, R. DeVore, G. Kerkyacharian and D. Picard, Maximal spaces with given rate of convergence for thresholding algorithms. Appl. Comput. Harmon. Anal. 11 (2001) 167–191. [Google Scholar]
  6. I. Daubechies, Orthonormal bases of compactly supported wavelets. Comm. Pure Appl. Math. 41 (1988) 909–996. [Google Scholar]
  7. P. Dodos, Dichotomies of the set of test measures of a Haar-null set. Isr. J. Math. 144 (2004) 15–28. [CrossRef] [Google Scholar]
  8. D. Donoho and I. Johnstone, Minimax risk over lp-balls for lq-error. Probab. Theory Relat. Fields 99 (1994) 277–303. [CrossRef] [Google Scholar]
  9. D. Donoho and I. Johnstone, Minimax estimation via wavelet shrinkage. Ann. Stat. 26 (1998) 879–921. [Google Scholar]
  10. D.L. Donoho, I.M. Johnstone, G. Kerkyacharian and D. Picard, Universal near minimaxity of wavelet shrinkage. Festschrift for Lucien Le Cam, Springer, New York (1997) 183–218. [Google Scholar]
  11. A. Fraysse, Generic validity of the multifractal formalism. SIAM J. Math. Anal. 37 (2007) 593–607. [CrossRef] [Google Scholar]
  12. B. Hunt, The prevalence of continuous nowhere differentiable function. Proc. Am. Math. Soc. 122 (1994) 711–717. [Google Scholar]
  13. B. Hunt, T. Sauer and J. Yorke, Prevalence: a translation invariant “almost every” on infinite dimensional spaces. Bull. Am. Math. Soc. 27 (1992) 217–238. [CrossRef] [Google Scholar]
  14. I.A. Ibragimov and R.Z. Hasminski, Statistical estimation, Applications of Mathematics, vol. 16. Springer-Verlag (1981). [Google Scholar]
  15. S. Jaffard, Old friends revisited: The multifractal nature of some classical functions. J. Fourier Anal. Appl. 3 (1997) 1–22. [Google Scholar]
  16. S. Jaffard, On the Frisch-Parisi conjecture. J. Math. Pures Appl. 79 (2000) 525–552. [CrossRef] [Google Scholar]
  17. G. Kerkyacharian and D. Picard, Density estimation by kernel and wavelets methods: optimality of Besov spaces. Stat. Probab. Lett. 18 (1993) 327–336. [Google Scholar]
  18. G. Kerkyacharian and D. Picard, Thresholding algorithms, maxisets and well-concentrated bases. Test 9 (2000) 283–344, With comments, and a rejoinder by the authors. [CrossRef] [MathSciNet] [Google Scholar]
  19. G. Kerkyacharian and D. Picard, Minimax or maxisets? Bernoulli 8 (2002) 219–253. [MathSciNet] [Google Scholar]
  20. S. Mallat, A wavelet tour of signal processing. Academic Press, San Diego, CA (1998) xxiv. [Google Scholar]
  21. Y. Meyer, Ondelettes et opérateurs. Hermann (1990). [Google Scholar]
  22. A.S. Nemirovskiĭ, B.T. Polyak and A.B. Tsybakov, The rate of convergence of nonparametric estimates of maximum likelihood type. Problemy Peredachi Informatsii 21 (1985) 17–33. [Google Scholar]
  23. M.S. Pinsker, Optimal filtration of square-integrable signals in Gaussian noise. Probl. Infor. Transm. 16 (1980) 52–68. [Google Scholar]
  24. V. Rivoirard, Maxisets for linear procedures, Stat. Probab. Lett. 67 (2004) 267–275. [Google Scholar]
  25. V. Rivoirard, Nonlinear estimation over weak Besov spaces and minimax Bayes method, Bernoulli 12 (2006) 609–632. [CrossRef] [MathSciNet] [Google Scholar]
  26. E. Stein, Singular integrals and differentiability properties of functions. Princeton University Press (1970). [Google Scholar]
  27. A. Tsybakov, Introduction to nonparametric estimation. Springer Series in Statistics, Springer, New York (2009). [Google Scholar]
  28. A. Van der Vaart, Asymptotic statistics, Cambridge Series in Statistical and Probabilistic Mathematics, vol. 3. Cambridge University Press (1998). [Google Scholar]

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.