Worst possible sub-directions in high-dimensional models

@article{Geer2016WorstPS,
  title={Worst possible sub-directions in high-dimensional models},
  author={S. Geer},
  journal={J. Multivar. Anal.},
  year={2016},
  volume={146},
  pages={248-260}
}
  • S. Geer
  • Published 2016
  • Computer Science, Mathematics
  • J. Multivar. Anal.
We examine the rate of convergence of the Lasso estimator of lower dimensional components of the high-dimensional parameter. Under bounds on the ? 1 -norm on the worst possible sub-direction these rates are of order | J | log p / n where p is the total number of parameters, n is the number of observations and J ? { 1 , ? , p } represents a subset of the parameters. We also derive rates in sup-norm in terms of the rate of convergence in ? 1 -norm. The irrepresentable condition on a set J… Expand
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