We consider the following sparse signal recovery (or feature selection) problem: given a design matrix X ∈ R n×m (m ≫ n) and a noisy observation vector y ∈ R n satisfying y = Xβ * + ε where ε is the noise vector following a Gaussian distribution N(0, σ 2 I), how to recover the signal (or parameter vector) β * when the signal is sparse? The Dantzig selector has been proposed for sparse signal recovery with strong theoretical guarantees. In this paper, we propose a multi-stage Dantzig selector

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... hod, which iteratively refines the target signal β * . We show that if X obeys a certain condition, then with a large probability the difference between the solution β estimated by the proposed method and the true solution β * measured in terms of the ℓ p norm (p ≥ 1) is bounded as where C is a constant, s is the number of nonzero entries in β * , the risk of the oracle estimator ∆ is independent of m and is much smaller than the first term, and N is the number of entries of β * larger than a certain value in the order of O(σ √ log m). The proposed method improves the estimation bound of the standard Dantzig selector approximately from Cs 1/p √ log mσ to C(s − N) 1/p √ log mσ where the value N depends on the number of large entries in β * . When N = s, the proposed algorithm achieves the oracle solution with a high probability, where the oracle solution is the projection of the observation vector y onto true features. In addition, with a large probability, the proposed method can select the same number of correct features under a milder condition than the Dantzig selector. Finally, we extend this multi-stage procedure to the LASSO case.