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A number of fundamental results in modern statistical theory involve thresholding estimators. This survey paper aims at reconstructing the history of how thresholding rules came to be popular in stati...
The effect of errors in variables in quantization is investigated. We prove general exact and non-exact oracle inequalities with fast rates for an empirical minimization based on a noisy sample $Z_i=X...
We analyze general model selection procedures using penalized empirical loss minimization under computational constraints. While classical model selection approaches do not consider computational aspe...
To better understand the interplay of censoring and sparsity we develop finite sample properties of nonparametric Cox proportional hazard乫s model. Due to high impact of sequencing data, carrying genet...
We study high-dimensional linear models and the $\ell_1$-penalized least squares estimator, also known as the Lasso estimator.
We provide new methods for estimation of the one-point specification probabilities in general discrete random fields.
An adaptive nonparametric estimation procedure is constructed for heteroscedastic regression when the noise variance depends on the unknown regression. A non-asymptotic upper bound for a quadratic ...
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 sparsity or...
We propose a general family of algorithms for regression estimation with quadratic loss, on the basis of geometrical considerations. These algorithms are able to select relevant functions into a large...
Model selection is often performed by empirical risk minimization. The quality of selection in a given situation can be assessed by risk bounds, which require assumptions both on the margin and the ta...
This paper studies oracle properties of ℓ1-penalized least squares in nonparametric regression setting with random design. We show that the penalized least squares estimator satisfies sparsity...
In this paper we study the problem of adaptive estimation of a multivariate function satisfying some structural assumption. We propose a novel estimation procedure that adapts simultaneously to unkn...

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