2007/01/01 by Florentina Bunea, Alexandre Tsybakov, Marten Wegkamp · 6 citations
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Dimension (graph theory) #Estimator #Lasso (programming language) #Least-squares function approximation #Linear regression #Nonparametric regression #Nonparametric statistics #Oracle #Statistical Methods and Inference #Stochastic Gradient Optimization Techniques #math.ST #msc:62C20 #msc:62G05 #msc:62G08 #msc:62G20 #stat.TH
paper · pdf · doi:10.1214/07-ejs008
published as Electronic Journal of Statistics 2007, Vol. 1, 169-194 · Published at http://dx.doi.org/10.1214/07-EJS008 in the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2007/01/01 · arxiv created 2007/05/23 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 oracle inequalities, i.e., bounds in terms of the number of non-zero components of the oracle vector. The results are valid even when the dimension of the model is (much) larger than the sample size and the regression matrix is not positive definite. They can be applied to high-dimensional linear regression, to nonparametric adaptive regression estimation and to the problem of aggregation of arbitrary estimators.