Journal
ELECTRONIC JOURNAL OF STATISTICS
Volume 3, Issue -, Pages 1360-1392Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/09-EJS506
Keywords
Coherence; compatibility; irrepresentable condition; Lasso; restricted eigenvalue; restricted isometry; sparsity
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Oracle inequalities and variable selection properties for the Lasso in linear models have been established under a variety of different assumptions on the design matrix. We show in this paper how the different conditions and concepts relate to each other. The restricted eigenvalue condition [2] or the slightly weaker compatibility condition [18] are sufficient for oracle results. We argue that both these conditions allow for a fairly general class of design matrices. Hence, optimality of the Lasso for prediction and estimation holds for more general situations than what it appears from coherence [5, 4] or restricted isometry [10] assumptions.
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