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Abstract: statistical estimation The goal of this section is to prove a lemma that will help to establish the main forthcoming results of the paper. The material presented here closely follows the concept of oracle inequalities developed by Donoho and Johnstone (1994). 10 Suppose that we have the following problem: y i = # i + #z i , i # I, (4.1) where for any finite subset I # I, {z i } i#I is a Gaussian vector with mean 0 and covariance matrix V i,j . In this section, I might be finite or... (Update)
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BibTeX entry: (Update)
@misc{ candes-ridgelets,
author = "Emmanuel J. Candes",
title = "Ridgelets: Estimating with Ridge Functions",
url = "citeseer.ist.psu.edu/383955.html" }
Citations (may not include all citations):357 Approximation by superpositions of a sigmoidal function (context) - Cybenko - 1989
243 Ideal spatial adaptation via wavelet shrinkage (context) - Donoho, Johnstone - 1994
186 Projection pursuit regression (context) - Friedman, Stuetzle - 1981
134 Minimax estimation via wavelet shrinkage - Donoho, Johnstone - 1998
126 Applied nonparametric regression (context) - Hardle - 1990
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69 Neural networks: a review from a statistical perspective (context) - Cheng, Titterington - 1994
59 The Radon transform and some of its applications (context) - Deans - 1983
50 Minimax theory of image reconstruction (context) - Korostelev, Tsybakov - 1993
33 Optimal filtering of square-integrable signals in gaussian w.. (context) - Pinsker - 1980
31 Statistical estimation (context) - Ibragimov, Hasminskii - 1981
20 Projection-based approximation and a duality with kernel met.. (context) - Donoho, Johnstone - 1989
16 Ridgelets: theory and applications (context) - Candes - 1998
12 Empirical atomic decomposition (context) - Donoho, Johnstone - 1995
9 Wavelets in statistics: beyond the standard assumptions - Silverman - 1999
8 the infeasibility of training neural networks with small mea.. (context) - Vu - 1998
8 New York: Springer-Verlag (context) - Hardle, Kerkyacharian et al. - 1998
6 Applied and Computational Harmonic Analysis (context) - Candes
6 Monoscale ridgelets for the representation of images with ed.. (context) - Candes
4 Estimation of square-integrable [spectral] density based on .. (context) - Efroimovich, Pinsker - 1982
3 Consistent nonparametric regression (context) - Soc, Stone - 1977
3 Department of Statistics (context) - Candes, Donoho - 1999
2 the representation of mutilated sobolev functions (context) - Department, Stanford et al.
2 Ridgelet representations of new smoothness classes (context) - Candes
2 New York: Springer-Verlag (context) - comments, by et al. - 1988
2 Wavelets and operators (context) - York, Meyer - 1992
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