Minimax rates of estimation for high-dimensional linear regression over lq-balls
نویسندگان
چکیده
Consider the high-dimensional linear regression model y = Xβ∗ +w, where y ∈ R is an observation vector, X ∈ R is a design matrix with d > n, the quantity β∗ ∈ R is an unknown regression vector, and w ∼ N (0, σI) is additive Gaussian noise. This paper studies the minimax rates of convergence for estimating β∗ in either l2-loss and l2-prediction loss, assuming that β∗ belongs to an lq-ball Bq(Rq) for some q ∈ [0, 1]. It is shown that under suitable regularity conditions on the design matrix X , the minimax optimal rate in l2-loss and l2-prediction loss scales as Rq (
منابع مشابه
Minimax rates of estimation for high-dimensional linear regression over $\ell_q$-balls
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