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Journal of Econometrics, ISSN 0304-4076, 06/2015, Volume 186, Issue 2, pp. 325 - 344
This paper establishes non-asymptotic oracle inequalities for the prediction error and estimation accuracy of the LASSO in stationary vector autoregressive... 
High-dimensional data | Oracle inequality | VAR | Adaptive LASSO | LASSO | REGRESSION | VARIABLE SELECTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SHRINKAGE | MODEL SELECTION | BRIDGE ESTIMATORS | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS
Journal Article
Journal Article
IEEE Transactions on Information Theory, ISSN 0018-9448, 04/2011, Volume 57, Issue 4, pp. 2342 - 2359
Journal Article
BERNOULLI, ISSN 1350-7265, 05/2019, Volume 25, Issue 2, pp. 1225 - 1255
The abundance of high-dimensional data in the modern sciences has generated tremendous interest in penalized estimators such as the lasso, scaled lasso,... 
high-dimensional regression | SPARSITY | oracle inequalities | RECOVERY | OPTIMAL RATES | MODEL SELECTION | LASSO | prediction | STATISTICS & PROBABILITY | REGRESSION SHRINKAGE | VARIABLE SELECTION | SLOPE
Journal Article
Annals of Statistics, ISSN 0090-5364, 02/2017, Volume 45, Issue 1, pp. 316 - 354
Inhomogeneous random graph models encompass many network models such as stochastic block models and latent position models. We consider the problem of... 
Networks | Inhomogeneous random graph | Oracle inequality | Sparsity | Sparse graphon | Stochastic block model | stochastic block model | oracle inequality | sparse graphon | STATISTICS & PROBABILITY | sparsity | networks | Statistics | Mathematics
Journal Article
Electronic Journal of Statistics, ISSN 1935-7524, 2007, Volume 1, pp. 169 - 194
This paper studies oracle properties of l(1)-penalized least squares in nonparametric regression setting with random design. We show that the penalized least... 
Aggregation | Dimension reduction | Sparsity | Lasso | Nonparametric regression | Mutual coherence | Adaptive estimation | Oracle inequalities | Penalized least squares | oracle inequalities | nonparametric regression | penalized least squares | mutual coherence | STATISTICS & PROBABILITY | sparsity | aggregation | dimension reduction | adaptive estimation | Probability | Mathematics
Journal Article
Neurocomputing, ISSN 0925-2312, 05/2017, Volume 239, pp. 214 - 222
We investigate properties of estimators obtained by minimization of -processes with the Lasso penalty in the high-dimensional setting. Our attention is focused... 
Penalized risk minimization | Oracle inequality | High-dimensional problem | U-process | Sparse model | Machine learning | MINIMIZATION | MODEL | SELECTION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Computer science | Analysis
Journal Article
The Annals of Statistics, ISSN 0090-5364, 6/2013, Volume 41, Issue 3, pp. 1142 - 1165
Journal Article
Electronic Journal of Probability, ISSN 1083-6489, 2015, Volume 20, p. 114
We study the dimension-free inequalities, see Talagrand [49], for non-product measures extending Marton's [39] weak transport from the Hamming distance to... 
Transport inequalities | Concentration of measures | Oracle inequalities | Time series | oracle inequalities | EMPIRICAL PROCESSES | DISTANCE | transport inequalities | time series | STATISTICS & PROBABILITY | concentration of measures | CHAINS | Mathematics
Journal Article
Annals of the Institute of Statistical Mathematics, ISSN 0020-3157, 2018, pp. 1 - 45
In this paper, we consider a high-dimensional statistical estimation problem in which the number of parameters is comparable or larger than the sample size. We... 
High-dimensional estimation | Oracle inequality | Penalized estimation | Low-complexity models | Exponential weighted aggregation | Statistical analysis | Estimating techniques | Estimators | Inequalities | Data loss | Complexity | Statistics | Mathematics
Journal Article
The Annals of Statistics, ISSN 0090-5364, 6/2011, Volume 39, Issue 3, pp. 1608 - 1632
We address the problem of density estimation with 𝕃 s -loss by selection of kernel estimators. We develop a selection procedure and derive corresponding 𝕃 s... 
Density estimation | Minimax | Estimate reliability | Mathematical inequalities | Mathematical functions | Density | Estimators | Oracles | Double-struck L | Kernel estimators | Empirical process | risk | Adaptive estimation | Oracle inequalities | oracle inequalities | L-s-risk | kernel estimators | empirical process | STATISTICS & PROBABILITY | adaptive estimation | Mathematics | 62G05 | Ls-risk | 62G20
Journal Article
Computational Mathematics and Mathematical Physics, ISSN 0965-5425, 5/2019, Volume 59, Issue 5, pp. 836 - 841
A novel analog of Nemirovski’s proximal mirror method with an adaptive choice of constants in the minimized prox-mappings at each iteration for variational... 
Computational Mathematics and Numerical Analysis | proximal method | inexact oracle | adaptive method | Mathematics | variational inequality | Hölder continuous field operator | MATHEMATICS, APPLIED | Holder continuous field operator | PHYSICS, MATHEMATICAL | Algorithms | Information management | Analysis | Methods | Resveratrol | Inequalities
Journal Article
Annals of Statistics, ISSN 0090-5364, 2017, Volume 45, Issue 1, pp. 316 - 354
Inhomogeneous random graph models encompass many network models such as stochastic block models and latent position models. We consider the problem of... 
Modeling and Simulation | Computer Science | Automatic Control Engineering
Journal Article
IEEE Transactions on Information Theory, ISSN 0018-9448, 03/2019, Volume 65, Issue 3, pp. 1452 - 1472
Journal Article
Bernoulli, ISSN 1350-7265, 8/2009, Volume 15, Issue 3, pp. 799 - 828
Let $Y_{j}=f_{\ast}(X_{j})+\xi _{j},\quad j=1,\ldots ,n$ , where $X,X_{1},\ldots ,X_{n}$ are i.i.d. random variables in a measurable space (S, ${\cal A}$ )... 
Dictionaries | Logical proofs | Mathematical constants | Coordinate systems | Mathematical vectors | Mathematical inequalities | Random variables | Regression analysis | Estimators | Oracles | Regression | Sparsity | Oracle inequalities | Dantzig selector | LARGE UNDERDETERMINED SYSTEMS | oracle inequalities | regression | RECONSTRUCTION | EQUATIONS | STATISTICS & PROBABILITY | sparsity
Journal Article
Annals of Statistics, ISSN 0090-5364, 02/2019, Volume 47, Issue 1, pp. 233 - 287
We study the problem of nonparametric estimation under L-p-loss, p is an element of[1, infinity), in the framework of the convolution structure density model... 
Deconvolution model | Density estimation | Kernel estimators | Anisotropic Nikol’skii class | Adaptive estimation | Oracle inequality | Lp-risk | anisotropic Nikol'skii class | oracle inequality | STATISTICS & PROBABILITY | L-p-risk | RATES | DECONVOLUTION | kernel estimators | BOUNDS | ADAPTATION | CONVERGENCE | SELECTION | density estimation | adaptive estimation | Statistics | Mathematics
Journal Article
Statistical Inference for Stochastic Processes, ISSN 1387-0874, 7/2018, Volume 21, Issue 2, pp. 469 - 483
Journal Article
The Annals of Statistics, ISSN 0090-5364, 6/2002, Volume 30, Issue 3, pp. 843 - 874
Journal Article
IEEE Transactions on Information Theory, ISSN 0018-9448, 07/2010, Volume 56, Issue 7, pp. 3516 - 3522
Journal Article
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