Maximal Spaces with Given Rate of Convergence for Thresholding Algorithms

Applied and Computational Harmonic Analysis

Volumn 11, Issue 2, 2001, Pages 167-191

  Cohen, Albert ^a   Devore, Ronald ^b   Kerkyacharian, Gerard ^c   Picard, Dominique ^d  

^a SORBONNE UNIVERSITÉ   (France)

^b UNIVERSITY OF SOUTH CAROLINA   (United States)

^c UNIVERSITÉ PARIS OUEST NANTERRE LA DÉFENSE   (France)

^d UNIVERSITÉ PARIS DESCARTES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035446697     PISSN: 10635203     EISSN: None     Source Type: Journal    
DOI: 10.1006/acha.2000.0333     Document Type: Article

References (26)

1. Cohen A., Daubechies I., Vial P. Wavelets and fast wavelet transforms on an interval. Appl. Comput. Harmon. Anal. 1:1993.
2. Cohen A., DeVore R., Hochmuth R. Restricted nonlinear approximation. Construct. Approx. 16:2000;85-113.
3. Cohen A. Wavelets in numerical analysis. Ciarlet P. G., Lions J. L. Handbook of Numerical Analysis. 2000;Elsevier, Amsterdam.
4. Daubechies I. Ten Lectures on Wavelets. 1992;SIAM, Philadelphia.
5. Donoho D. L., Johnstone I. M. Minimax estimation via wavelet shrinkage. Ann. Statist. 26:1998;879-921.
6. Donoho D. L., Johnstone I. M. Adapting to unknown smoothness via wavelet shrinkage. J. Amer. Statist. Assoc. 90:1995;1200-1224.
7. Donoho D. L., Johnstone I. M., Kerkyacharian G., Picard D. Wavelet shrinkage: Asymptopia? J. Roy. Statist. Soc. 57:1996;301-369.
8. Donoho D. L., Johnstone I. M., Kerkyacharian G., Picard D. Density estimation by wavelet thresholding. Ann. Statist. 24:1996;508-539.
9. Donoho D. L., Johnstone I. M. Neoclassical minimax problems, thresholding and adaptive function estimation. Bernoulli. 1:1996;39-62.
10. DeVore R., Jawerth B., Popov V. Compression of wavelet decompositions. Amer. J. Math. 114:1991;737-785.
11. Hall P., Kerkyacharian G., Picard D. On block thresholding rules for curve estimation using wavelet methods. Ann. Statist. 26:1996;922-942.
12. Johnstone I. M., Kerkyacharian G., Picard D. Estimation d'une densité de probabilité par méthode d'ondelettes. Compt. Rend. Acad. Sci. Paris (A). 315:1992;211-216.
13. Kerkyacharian G., Picard D. Density estimation in Besov spaces. Statist. Probab. Lett. 13:1992;15-24.
14. Kerkyacharian G., Picard D. Density estimation by kernel and wavelets methods - Optimality of Besov spaces. Statist. Probab. Lett. 18:1993;327-336.
15. p adaptive density estimation. Bernoulli. 2:1996;229-247.
16. Lepskii O. V. Asymptotically minimax adaptive estimation I: Upper bounds. Optimally adaptive estimates. Theory Probab. Appl. 36:1991;682-697.
17. Meyer Y. Ondelettes et Opérateurs. 1990;Hermann, Paris.
18. A. S. Nemirovskii, Nonparametric estimation of smooth regression functions, Izv. Akad. Nauk. SSSR Techn. Kibernet.31985, 50-60 [in Russian]; J. Comput. Syst. Sci.231986, 1-11 [in English].
19. A. S. Nemirovskii, Nonparametric estimation of smooth regression functions, Izv. Akad. Nauk. SSSR Techn. Kibernet.31985, 50-60 [in Russian]; J. Comput. Syst. Sci.231986, 1-11 [in English].
20. 2. Ann. Statist. 13:1985;984-997.
21. Peetre J. New thoughts on Besov spaces. Duke Univ. Math. Ser. 1:1975.
22. M. S. Pinsker, Optimal filtering of square integrable signals in Gaussian white noise, Probl. Pered. Inform.161980, 52-68 [in Russian]; Probl. Inform. Trans.1980, 120-133 [in English].
23. M. S. Pinsker, Optimal filtering of square integrable signals in Gaussian white noise, Probl. Pered. Inform.161980, 52-68 [in Russian]; Probl. Inform. Trans.1980, 120-133 [in English].
24. Scott D. W. Multivariate Density Estimation. 1992;Wiley, New York.
25. Stone C. Optimal global rates of convergence for nonparametric estimates. Ann. Statist. 10:1982;1040-1053.
26. Temlyakov V. The best m-term approximation and greedy algorithms. Adv. Comput. Math. 8:1997;249-265.