Sparsity oracle inequalities for the Lasso

  title={Sparsity oracle inequalities for the Lasso},
  author={Florentina Bunea and Alexandre B. Tsybakov and Marten H. Wegkamp},
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… CONTINUE READING
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