Minimax rates of ℓ_p-losses for high-dimensional linear regression models with additive measurement errors over ℓ_q-balls

11/19/2019

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by   Xin Li, et al.

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We study minimax rates for high-dimensional linear regression with additive errors under the ℓ_p (1≤ p<∞)-losses, where the regression parameter is of weak sparsity. Our lower and upper bounds agree up to constant factors, implying that the proposed estimator is minimax optimal.