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The Annals of statistics, ISSN 0090-5364, 2016, Volume 44, Issue 6, pp. 2695 - 2725
Journal Article
Annals of Statistics, ISSN 0090-5364, 2018, Volume 46, Issue 6B, pp. 3767 - 3804
Journal Article
The Annals of statistics, ISSN 0090-5364, 2011, Volume 39, Issue 2, pp. 1282 - 1309
We introduce a new criterion, the Rank Selection Criterion (RSC), for selecting the optimal reduced rank estimator of the coefficient matrix in multivariate response regression models... 
Minimax | Linear regression | Least squares | Signal noise | Matrices | Coefficients | Estimators | Consistent estimators | Oracles | Estimation methods | reduced rank estimators | REGRESSION | oracle inequalities | rank selection | nuclear norm | Multivariate response regression | STATISTICS & PROBABILITY | dimension reduction | adaptive estimation | low rank matrix approximation | 62H15 | 62J07
Journal Article
Journal of the Royal Statistical Society. Series B, Statistical methodology, ISSN 1369-7412, 2017, Volume 79, Issue 3, pp. 939 - 956
.... Indeed, the standard lasso estimator or Dantzig selector turns out to become unreliable when only noisy regressors are available, which is quite common in practice... 
Matrix uncertainty selector | Prediction sensitivity | Linear regression model | Conic programming | Dantzig selector | REGRESSION | LASSO | STATISTICS & PROBABILITY | Studies | Linear programming | Statistical methods | Permissible error | Minimax technique | Minimization | Mathematical models | Regression analysis | Estimators | Optimization | Samples | Programming | Regression | Polynomials
Journal Article
Physical Review Letters, ISSN 0031-9007, 03/2016, Volume 116, Issue 9, p. 090407
A minimax estimator has the minimum possible error ("risk") in the worst case. We construct the first minimax estimators for quantum state tomography with relative entropy risk... 
PHYSICS, MULTIDISCIPLINARY | Minimax technique | Construction | Tomography | Risk | Entropy | Sampling | Estimates | Estimators | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Journal Article
IEEE Transactions on Image Processing, ISSN 1057-7149, 04/2017, Volume 26, Issue 4, pp. 1637 - 1649
A non-local means (NLM) filter is a weighted average of a large number of non-local pixels with various image intensity values. The NLM filters have been shown... 
Smoothing methods | PSNR | Noise reduction | Estimation | Noise measurement | image denoising | James-Stein estimator | bounded self-weight | Upper bound | Gaussian noise | non-local means | center pixel weight | minimax estimator | FILTER | INFORMATION | MULTIVARIATE NORMAL-DISTRIBUTION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Noise | Research
Journal Article
The Annals of statistics, ISSN 0090-5364, 2011, Volume 39, Issue 1, pp. 201 - 231
Journal Article
Biometrika, ISSN 0006-3444, 6/2012, Volume 99, Issue 2, pp. 315 - 325
.... In this paper, we give sufficient conditions under which a local minimizer is unique, and show that the oracle estimator becomes the unique local minimizer with probability... 
Regression coefficients | Minimax | Sufficient conditions | Estimate reliability | Uniqueness | Eigenvalues | Convexity | Unbiased estimators | Estimators | Oracles | Minimax concave penalty | Oracle estimator | Smoothly clipped absolute deviation | Regularization | Global optimality | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | STATISTICS & PROBABILITY | VARIABLE SELECTION | LIKELIHOOD | Computer applications
Journal Article
Journal of Theoretical Biology, ISSN 0022-5193, 10/2015, Volume 383, pp. 106 - 115
In this paper, decision theory was used to derive Bayes and minimax decision rules to estimate allelic frequencies and to explore their admissibility. Decision... 
Bayes estimators | Minimax estimators | Admissible estimators | Average risk | Decision theory | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | Data Interpretation, Statistical | Models, Genetic | Algorithms | Gene Frequency | Humans | Bayes Theorem | Decision-making | Analysis
Journal Article
IEEE Transactions on Communications, ISSN 0090-6778, 09/2015, Volume 63, Issue 9, pp. 3350 - 3362
Journal Article
Annals of Statistics, ISSN 0090-5364, 04/2018, Volume 46, Issue 2, pp. 745 - 780
The performance of Least Squares (LS) estimators is studied in shape-constrained regression models under Gaussian and sub-Gaussian noise... 
Minimax rates | Concentration | Convexity | Gaussian width | Shape restricted regression | CONVEX REGRESSION | RISK BOUNDS | STATISTICS & PROBABILITY | concentration | minimax rates | convexity
Journal Article
Journal of the Royal Statistical Society: Series B (Statistical Methodology), ISSN 1369-7412, 09/2019, Volume 81, Issue 4, pp. 735 - 761
Journal Article
Automatica, ISSN 0005-1098, 09/2017, Volume 83, pp. 133 - 140
.... Then, the robust estimator is obtained by minimizing the mean square error according to the least favorable statistics in that ball... 
Tau divergence family | Robust filtering | Minimum entropy problem | Risk-sensitive estimation problem | Minimax problem | PERTURBATIONS | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC
Journal Article
The Annals of Statistics, ISSN 0090-5364, 8/2012, Volume 40, Issue 4, pp. 2327 - 2355
Journal Article
Journal of Statistical Planning and Inference, ISSN 0378-3758, 2008, Volume 138, Issue 10, pp. 2906 - 2917
Journal Article
Statistics and Probability Letters, ISSN 0167-7152, 01/2015, Volume 96, pp. 241 - 246
We consider minimax shrinkage estimation of location for spherically symmetric distributions under a concave function of the usual squared error loss. Scale... 
Concave loss | Minimaxity | Stein estimation | Location parameters | Secondary | Primary | SPHERICALLY SYMMETRIC DISTRIBUTIONS | MINIMAX ESTIMATION | MULTIVARIATE NORMAL-DISTRIBUTION | QUADRATIC LOSS | STATISTICS & PROBABILITY
Journal Article
Bernoulli, ISSN 1350-7265, 02/2017, Volume 23, Issue 1, pp. 219 - 248
... under a simple boundedness assumption and we show that the rate is optimal in a minimax sense. Unlike the procedures based on exponential weights, this estimator is fully adaptive under the uniform prior... 
Aggregation | Density estimation | Model selection | Sharp oracle inequality | Concentration inequality | Minimax lower bounds | Minimax optimality | minimax optimality | minimax lower bounds | sharp oracle inequality | EMPIRICAL RISK MINIMIZATION | concentration inequality | model selection | STATISTICS & PROBABILITY | aggregation | SPARSE ESTIMATION | SHARP ORACLE INEQUALITIES | density estimation | AFFINE ESTIMATORS
Journal Article
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