Oracle Inequalities for High-dimensional Prediction

@article{Lederer2016OracleIF,
  title={Oracle Inequalities for High-dimensional Prediction},
  author={Johannes Lederer and Lu Yu and Irina Gaynanova},
  journal={arXiv: Statistics Theory},
  year={2016}
}
The abundance of high-dimensional data in the modern sciences has generated tremendous interest in penalized estimators such as the lasso, scaled lasso, square-root lasso, elastic net, and many others. In this paper, we establish a general oracle inequality for prediction in high-dimensional linear regression with such methods. Since the proof relies only on convexity and continuity arguments, the result holds irrespective of the design matrix and applies to a wide range of penalized estimators… Expand
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