Estimation Error of the Lasso
نویسندگان
چکیده
This paper presents an upper bound for the estimation error of the constrained lasso, under the high-dimensional (n < p) setting. In contrast to existing results, the error bound in this paper is sharp, is valid when the parameter to be estimated is not exactly sparse (e.g., when the parameter is weakly sparse), and shows explicitly the effect of over-estimating the `1-norm of the parameter to be estimated on the estimation performance of the lasso. The results of this paper show that the lasso is minimax optimal for estimating a parameter with bounded `1-norm, and if the exact value of the `1-norm of the parameter to be estimated is accessible, the lasso is also minimax optimal for estimating a weakly sparse parameter.
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