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

Dongya Wu; Xin Li

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

Xin Li , Dongya Wu This is my paper · ORCID

classification math.STstat.TH

keywords minimaxregressionadditiveerrorshigh-dimensionallinearlossesrates

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abstract

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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