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Introduction to Nonparametric Estimation
  • A. Tsybakov
  • Computer Science, Mathematics
  • Springer series in statistics
  • 22 October 2008
This is a concise text developed from lecture notes and ready to be used for a course on the graduate level. Expand
We show that, under a sparsity scenario, the Lasso estimator and the Dantzig selector exhibit similar behavior. For both methods, we derive, in parallel, oracle inequalities for the prediction riskExpand
Smooth Discrimination Analysis
Discriminant analysis for two data sets in IRd with probability densities f and g can be based on the estimation of the set G = {x : f(x) I g(x)}. We consider applications where it is appropriate toExpand
Nuclear norm penalization and optimal rates for noisy low rank matrix completion
This paper deals with the trace regression model where $n$ entries or linear combinations of entries of an unknown $m_1\times m_2$ matrix $A_0$ corrupted by noise are observed. We propose a newExpand
Fast learning rates for plug-in classifiers
It has been recently shown that, under the margin (or low noise) assumption, there exist classifiers attaining fast rates of convergence of the excess Bayes risk, that is, rates faster than n -1/2 .Expand
Minimax theory of image reconstruction
Image processing is an increasingly important area of research and there exists a large variety of image reconstruction methods proposed by different authors. This book is concerned with a techniqueExpand
Exponential Screening and optimal rates of sparse estimation
In high-dimensional linear regression, the goal pursued here is to estimate an unknown regression function using linear combinations of a suitable set of covariates. One of the key assumptions forExpand
Optimal Rates of Aggregation
We study the problem of aggregation of M arbitrary estimators of a regression function with respect to the mean squared risk. Expand
Oracle Inequalities and Optimal Inference under Group Sparsity
We consider the problem of estimating a sparse linear regression vector s* under a gaussian noise model, for the purpose of both prediction and model selection. We assume that prior knowledge isExpand
Sparsity oracle inequalities for the Lasso
This paper studies oracle properties of $\ell_1$-penalized least squares in nonparametric regression setting with random design. We show that the penalized least squares estimator satisfies sparsityExpand