SLOPE is Adaptive to Unknown Sparsity and Asymptotically Minimax

@article{Cands2015SLOPEIA,
  title={SLOPE is Adaptive to Unknown Sparsity and Asymptotically Minimax},
  author={Emmanuel J. Cand{\`e}s and Weijie Su},
  journal={CoRR},
  year={2015},
  volume={abs/1503.08393}
}
We consider high-dimensional sparse regression problems in which we observe y = Xβ + z, where X is an n × p design matrix and z is an n-dimensional vector of independent Gaussian errors, each with variance σ. Our focus is on the recently introduced SLOPE estimator [15], which regularizes the least-squares estimates with the rank-dependent penalty ∑ 1≤i≤p λi|β̂|(i), where |β̂|(i) is the ith largest magnitude of the fitted coefficients. Under Gaussian designs, where the entries of X are i.i.d. N… CONTINUE READING
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