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• W2092199153 abstract "We consider the model y = Xθ∗ + ξ, Z = X + Ξ, where the random vector y ∈ ℝn and the random n × p matrix Z are observed, the n × p matrix X is unknown, Ξ is an n × p random noise matrix, ξ ∈ ℝn is a noise independent of Ξ, and θ∗ is a vector of unknown parameters to be estimated. The matrix uncertainty is in the fact that X is observed with additive error. For dimensions p that can be much larger than the sample size n, we consider the estimation of sparse vectors θ∗. Under matrix uncertainty, the Lasso and Dantzig selector turn out to be extremely unstable in recovering the sparsity pattern (i.e., of the set of nonzero components of θ∗), even if the noise level is very small. We suggest new estimators called matrix uncertainty selectors (or, shortly, the MU-selectors) which are close to θ∗ in different norms and in the prediction risk if the restricted eigenvalue assumption on X is satisfied. We also show that under somewhat stronger assumptions, these estimators recover correctly the sparsity pattern." @default.
• W2092199153 created "2016-06-24" @default.
• W2092199153 creator A5025419743 @default.
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• W2092199153 date "2010-10-01" @default.
• W2092199153 modified "2023-10-17" @default.
• W2092199153 title "Sparse recovery under matrix uncertainty" @default.
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• W2092199153 doi "https://doi.org/10.1214/10-aos793" @default.
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