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Much theoretical and applied work has been devoted to high-dimensional regression with clean data.
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[author] Zou, H.H. (2006). The Adaptive Lasso and Its Oracle Properties. Journal of the American Statistical Association 101 1418–1429
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[author] Candès, E.E. and Tao, T.T. (2007). The Dantzig Selector: Statistical Estimation When p Is Much Larger Than n. Annals of Statistics 35 2313–2351
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[author] Sørensen, Ø.Ø., Frigessi, A.A. and Thoresen, MM. (2013). Measurement Error in LASSO: Impact and Likelihood Bias Correction. Statistica sinica 23 Preprint
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