Minimax estimation via wavelet shrinkage

By David L. Donoho, Iain M. Johnstone. 1998

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Citations in the corpus

Additive models with trend filtering (2017, methodology): “Seminal theory from Donoho and Johnstone [1998] on minimax linear rates over Besov spaces shows that, under Assumption B2, and with the inputs X, i = 1, .”
Recovering edges in ill-posed inverse problems: optimality of curvelet frames (2002, background): “Without belaboring this point we can cite general theory [3, 55], examples of the very clean derivations of optimal procedures possible in the white noise model [58, 42, 57, 32, 24, 16, 18, 20, 27] and many successful applications of this principle to sampled data [33, 34, 55, 31, 29, 17, 28].”
Regularization in reinforcement learning (2011, methodology): “Kolter and Ng [2009] formulated an l1-regularization extension of LSTD and provided LARS-like algorithm [Efron et al., 2004] to efficiently compute the solutions. Taylor and Parr [2009] unified several kernelized reinforcement learning algorithms, and showed the equivalence of kernelized value funct”
SHRINKAGE, PRETEST AND ABSOLUTE PENALTY ESTIMATORS IN PARTIALLY LINEAR MODELS (2007, background): “Extending the language of Donoho & Johnstone (1998), β̂ PT 1 and β̂ S 1 are based on hard and smooth thresholdings, respectively.”
Adaptive Confidence Balls (2006, methodology): “In particular, for the Besov bodies Bβp,q(M) with p ≥ 2 Donoho and Johnstone [7] showed that the minimax linear risk is of order n−2β/(1+2β) and the methodology of Li [11] then leads to “honest” confidence balls with maximum expected squared radius converging at a rate of n−1/2 over Besov bodies Bβp”
The price of privacy and the limits of LP decoding (2007, background): “…privacy-preserving datamining our results say that any privacy mechanism, interactive or noninteractive, providing reasonably accurate answers to a 0.761 fraction of randomly generated weighted subset sum queries, and arbitrary answers on the remaining 0.239 fraction, is blatantly non-private.”
Wavelet methods for continuous-time prediction using Hilbert-valued autoregressive processes (2003, background): “In such cases, it is known that linear wavelet methods are not optimal (see, for example, [22]) and that one should seek nonlinear wavelet methods (see, for example, [1,5,6,43]).”
Nonquadratic estimators of a quadratic functional (2005, methodology): “In density estimation problems Donoho, Johnstone, Kerkyacharian and Picard [9] showed a similar phenomenon exists.”
Incorporating Information on Neighboring Coefficients Into Wavelet Estimation (2001, methodology): “1 Sequence space approximation We shall prove Theorem 1 and 2 by using the sequence space approach introduced by Donoho and Johnstone in [13].”
Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study (2001, background): “(Mathematically, all these function spaces can be formalized in terms of the socalled Besov or Triebel spaces; see, for example, Meyer (1992), Wojtaszczyk (1997), Donoho & Johnstone (1998) and Härdle, Kerkyacharian, Pickard & Tsybakov (1998).)”
Smooth Design-Adapted Wavelets for Nonparametric Stochastic Regression (2004, background): “Among these wavelet estimators, nonlinear thresholding schemes [20, 18, 19, 17] have been proved powerful and conceptually simple in order to have estimators which automatically adapt to spatially varying degrees of regularity of the underlying function to estimate.”