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文章基本信息

  • 标题:Sparsity oracle inequalities for the Lasso
  • 作者:Florentina Bunea ; Alexandre Tsybakov ; Marten H. Wegkamp
  • 期刊名称:Electronic Journal of Statistics
  • 印刷版ISSN:1935-7524
  • 出版年度:2007
  • 卷号:1
  • 页码:169-194
  • 出版社:Institute of Mathematical Statistics
  • 摘要: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 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.
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