Free Access
Volume 17, 2013
Page(s) 472 - 484
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]

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