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1,047
Minimax Estimation via Wavelet Shrinkage
, 1992
"... We attempt to recover an unknown function from noisy, sampled data. Using orthonormal bases of compactly supported wavelets we develop a nonlinear method which works in the wavelet domain by simple nonlinear shrinkage of the empirical wavelet coe cients. The shrinkage can be tuned to be nearly minim ..."
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Cited by 321 (29 self)
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minimax over any member of a wide range of Triebel and Besovtype smoothness constraints, and asymptotically minimax over Besov bodies with p q. Linear estimates cannot achieve even the minimax rates over Triebel and Besov classes with p <2, so our method can signi cantly outperform every linear
Blind Minimax Estimation
"... We consider the linear regression problem of estimating an unknown, deterministic parameter vector based on measurements corrupted by colored Gaussian noise. We present and analyze blind minimax estimators (BMEs), which consist of a bounded parameter set minimax estimator, whose parameter set is its ..."
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Cited by 18 (14 self)
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We consider the linear regression problem of estimating an unknown, deterministic parameter vector based on measurements corrupted by colored Gaussian noise. We present and analyze blind minimax estimators (BMEs), which consist of a bounded parameter set minimax estimator, whose parameter set
1 Blind Minimax Estimation
, 709
"... Abstract — We consider the linear regression problem of estimating an unknown, deterministic parameter vector based on measurements corrupted by colored Gaussian noise. We present and analyze blind minimax estimators (BMEs), which consist of a bounded parameter set minimax estimator, whose parameter ..."
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Abstract — We consider the linear regression problem of estimating an unknown, deterministic parameter vector based on measurements corrupted by colored Gaussian noise. We present and analyze blind minimax estimators (BMEs), which consist of a bounded parameter set minimax estimator, whose
Guaranteed Robust Nonlinear Minimax Estimation
, 2013
"... Abstract: Minimax parameter estimation aims at characterizing the set of all values of the parameter vector that minimize the largest absolute deviation between experimental data and corresponding model outputs. However, minimax estimation is well known to be extremely sensitive to outliers in the d ..."
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Cited by 15 (10 self)
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Abstract: Minimax parameter estimation aims at characterizing the set of all values of the parameter vector that minimize the largest absolute deviation between experimental data and corresponding model outputs. However, minimax estimation is well known to be extremely sensitive to outliers
Wedgelets: nearlyminimax estimation of edges
 Ann. Statist
, 1999
"... We study a simple “Horizon Model ” for the problem of recovering an image from noisy data; in this model the image has an edge with αHölder regularity. Adopting the viewpoint of computational harmonic analysis, we develop an overcomplete collection of atoms called wedgelets, dyadically organized in ..."
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Cited by 113 (8 self)
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special edgeletdecorated recursive partition which minimizes a complexitypenalized sum of squares. This estimate, using sufficient subpixel resolution, achieves nearly the minimax meansquared error in the Horizon Model. In fact, the method is adaptive in the sense that it achieves nearly the minimax
On Minimax Estimating Hilbert Random Elements∗
"... The problem of designing optimal algorithms for estimating random elements has received earlier considerable attention (Balakrishnan, 1976; Curtain and Pritchard, 1978; Ramm, 1996). Basically, these works deal with linear procedures and do not discuss the efficiency of nonlinear estimates. On the o ..."
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. On the other hand, the nonlinear optimal estimation algorithms are essentially based on using the true distribution of the random elements involved. Nevertheless, these obstacles of optimal methods can be overcome by means a minimax approach (Verdu ́ and Poor, 1984; Başar and Bernhard, 1991; Siemenikhin
ON ΓMINIMAX ESTIMATION WITH ORDERED OBSERVATIONS
"... SUMMARY. In this note we derive Γminimax estimators for the location parameter of the normal and uniform models. means belonging to a fixed interval form a class of priors, Γ. All distributions with uniformly bounded variances and We restrict ourselves to the rules which are linear combinations of ..."
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SUMMARY. In this note we derive Γminimax estimators for the location parameter of the normal and uniform models. means belonging to a fixed interval form a class of priors, Γ. All distributions with uniformly bounded variances and We restrict ourselves to the rules which are linear combinations
Minimax Estimation of Functionals of Discrete Distributions
, 2014
"... We propose a general framework for the construction and analysis of minimax estimators for a wide class of functionals of discrete distributions, where the alphabet size S is unknown and may be scaling with the number of observations n. We treat the respective regions where the functional is “nonsmo ..."
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We propose a general framework for the construction and analysis of minimax estimators for a wide class of functionals of discrete distributions, where the alphabet size S is unknown and may be scaling with the number of observations n. We treat the respective regions where the functional
Minimax estimators dominating the leastsquares estimator
 CONF. ACOUST., SPEECH, SIGNAL PROCESSING (ICASSP2005)
, 2005
"... We present several analytical and numerical results demonstrating the superiority of minimax estimators over leastsquares (LS) estimation. We show that, for any bounded parameter set, a linear minimax estimator achieves lower meansquared error than the LS estimator, over the entire parameter set. ..."
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Cited by 8 (5 self)
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We present several analytical and numerical results demonstrating the superiority of minimax estimators over leastsquares (LS) estimation. We show that, for any bounded parameter set, a linear minimax estimator achieves lower meansquared error than the LS estimator, over the entire parameter set
ASYMPTOTIC MINIMAX ESTIMATION IN NONPARAMETRIC AUTOREGRESSION
"... We develop asymptotic theory for nonparametric estimators of the autoregression function. To deal with irregularities in the pattern of explanatory variables caused by their randomness, we propose a new estimator which is a modification of the Priestley–Chao kernel method. It is shown that this esti ..."
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that this estimator has similar asymptotic properties to standard estimators of kernel type. We establish an asymptotic lower bound to the minimax risk in Sobolev classes and show that our modified Priestley–Chao estimator can get arbitrarily close to this efficiency bound. Key words: exact asymptotics, minimax risk
Results 1  10
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1,047