Minimax rates of $\ell_p$-losses for high-dimensional linear regression models with additive measurement errors over $\ell_q$-balls

Dongya Wu; Xin Li

arxiv: 1911.08063 · v1 · pith:T7OY44D7 · submitted 2019-11-19 · math.ST · stat.TH

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

Xin Li , Dongya Wu This is my paper

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classification math.ST stat.TH

keywords minimaxregressionadditiveerrorshigh-dimensionallinearlossesrates

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We study minimax rates for high-dimensional linear regression with additive errors under the $\ell_p\ (1\leq p<\infty)$-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.

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

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