On minimax wavelet estimators

Applied and Computational Harmonic Analysis

Volumn 3, Issue 3, 1996, Pages 215-228

  Delyon, B ^a   Juditsky, A ^a  

^a CAMPUS DE BEAULIEU   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000954086     PISSN: 10635203     EISSN: None     Source Type: Journal    
DOI: 10.1006/acha.1996.0017     Document Type: Article

References (26)

1. L. Andersson, N. Hall, B. Jawerth, and G. Peters, Wavelets on closed subsets of the real line, manuscript, 1993.
2. J. Bergh and J. Löfstrom, "Interpolation Spaces - An Introduction," Springer-Verlag, New York, 1976.
3. A. Cohen, I. Daubechies, B. Jawerth, and P. Vial, Multiresolution analysis, wavelets and fast algorithms on an interval, C. R. Acad. Sci. Paris 316 (1992), 417-421.
4. I. Daubechies, "Ten Lectures on Wavelets," Siam, Philadelphia, 1992.
5. B. Delyon and A. Juditsky, "On the Computation of Wavelet Coefficients," Technical Report 856, IRISA, Rennes, 1994.
6. p-Balls," Technical Report, Department of Statistics, Stanford University, 1992.
7. D. Donoho and I. Johnstone, "Minimax Estimation via Wavelet Shrinkage," Technical Report, Department of Statistics, Stanford University, 1992.
8. D. Donoho and I. Johnstone, "Adapting to Unknown Smoothness via Wavelet Shrinkage," Technical Report, Department of Statistics, Stanford University, 1993.
9. D. Donoho, I. Johnstone, G. Kerkyacharian, and D. Picard, Density estimation by wavelet thresholding, submitted, 1993.
10. D. Donoho, I. Johnstone, G. Kerkyacharian, and D. Picard, Wavelet Shrinkage: Asymptotia?, manuscript, 1993.
11. P. Doukan, "Mixing: Properties and Examples," Springer-Verlag, New York, 1993.
12. M. Frazier and B. Jawerth, "Littlewood-Paley Theory and the Study of Functional Spaces," CBSM Conf. Notes, Vol. 79, Amer. Math. Soc., Providence, 1991.
13. M. Freidlin and A. Ventzel, "Random Perturbations of Dynamical Systems," Springer-Verlag, New York, 1984.
14. Ibragimov and R. Khasminskij, "Statistical Estimation, Asymptotic Theory," Hauka, Moscow, Nauka, 1979 [Russian]; translation, Springer-Verlag, Berlin, 1981.
15. I. Johnstone, G. Kerkyacharian, and D. Picard, Estimation d'une densité de probabilité par méthode d'ondelettes, C. R. Acad. Sci. Paris (A) 315 (1992), 211-216.
16. A. Juditsky, "Wavelet Estimators: Adapting to Unknown Smoothness," Technical Report 815, IRISA, Rennes, 1994.
17. G. Kerkyacharian and D. Picard, Density estimation in Besov spaces, Statist. Probab. Lett. 13 (1992), 15-24.
18. O. Lepskij, Asymptotically minimax adaptive estimation I, TVIP 36, No. 4 (1991), 645-659 [Russian]; translated as SIAM J. Theory Probab. Appl.
19. O. Lepskij, Asymptotically minimax adaptive estimation I, TVIP 36, No. 4 (1991), 645-659 [Russian]; translated as SIAM J. Theory Probab. Appl.
20. Y. Meyer, Ondelettes, Hermann, Paris, 1990.
21. A. Nemirovskij, Nonparametric estimation of smooth regression functions, Izv. Acad. Nauk SSSR, Techn. Kibern. No. 3, 50-60, 1985 [Russian]; translated as J. Comput. System. Sci. 23, No. 6 (1986), 1-11.
22. A. Nemirovskij, Nonparametric estimation of smooth regression functions, Izv. Acad. Nauk SSSR, Techn. Kibern. No. 3, 50-60, 1985 [Russian]; translated as J. Comput. System. Sci. 23, No. 6 (1986), 1-11.
23. P. Oswald, On the degree of nonlinear spline approximations in Besov-Sobolev spaces, J. Approx. Theory 61 (1990), 131-157.
24. D. Pollard, "Convergence of Stochastic Processes," Springer-Verlag, New York/Berlin, 1984.
25. n, Forum. Math. 2 (1990), 451-476.
26. H. Triebel, "Theory of Function Spaces II," Birkhäuser, Berlin, 1992.