Nonlinear estimation in anisotropic multi-index denoising

Probability Theory and Related Fields

Volumn 121, Issue 2, 2001, Pages 137-170

  Kerkyacharian, Gérard ^a   Lepski, Oleg ^b   Picard, Dominique ^c  

^a UNIVERSITÉ PARIS OUEST NANTERRE LA DÉFENSE   (France)

^b AIX MARSEILLE UNIVERSITÉ   (France)

^c UNIVERSITÉ PARIS DESCARTES   (France)

Author keywords

Anisotropic besov spaces; Anisotropic smoothness; Curse of dimensionality; Denoising; Minimax rate of convergence; Nonparametric estimation

Indexed keywords

EID: 0035643281     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00008800     Document Type: Article

References (14)

1. Donoho, D.: Nonlinear solution of inverse problems by wavelet-vaguelet decomposition, Appl. Comput. Harm. An., 2, 101-126 (1995)
2. Granas, A.: Sur quelques methodes topologiques en analyse convexe, Nato advanced studies. Montreal., (1990)
3. Härdle, W., Kerkyacharian, G., Picard, D., Tsybakov, A.: Wavelet, Approximation and Statistical Applications Lecture Notes in Statistics v 129 Springer Verlag (1998)
4. Lepskii, O.V.: On one problem of adaptive estimation on white Gaussian noise, Teor. Veoryatnost. i Primenen., 35, 459-470 (in Russian). Theory of Probability and Appl., 35, 454-466 (in English) (1990)
5. Lepskii, O.V.: On one problem of adaptive estimation on white Gaussian noise, Teor. Veoryatnost. i Primenen., 35, 459-470 (in Russian). Theory of Probability and Appl., 35, 454-466 (in English) (1990)
6. Lepskii, O.V.: Asymptotically minimax adaptive estimation I: Upper bounds. Optimally adaptive estimates, Theory Probab. Appl., 36, 682-697 (1997)
7. Lepskii, O.V., Mammen, E., Spokoiny, V.G.: Optimal spatial adaptation to inhomogeneous smoothness: an approach based on kernel estimates with variable bandwidth selectors, Annals of Statistics., 25(3), 929-947 (1997)
8. Nikolskii S.M.: Approximation of functions of several variables and imbedding theorems (Russian). Sec. ed., Moskva, Nauka 1977 English translation of the first ed., Berlin 1975 (1975)
9. Neumann M.B.: Multivariate wavelet thresholding: A remedy against the curse of dimensionality? Technical report. (1998)
10. 2, Ann. Statist., 13, 984-997 (1985)
11. k, Theory Probab. Appl., 31(2), 118-125 (1986)
12. Skorohod, A.V.: Integration in Hilbert Spaces. Berlin, New York: Springer-Verlag (1974)
13. Tribouley, K.: Practical estimation of multivariate densities using wavelet methods, Statistica Neerlandica., 49, 41-62 (1995)
14. Walsh, J.B.: An Introduction to stochastic partial differential equations, École d'été de Probabilité de Saint Flour XIV, ed by Hennequin, Lecture Notes in Math., vol 1180. p 265-339 Berlin, Heidelberg, New York: Springer-Verlag (1984)