Rate Minimaxity of the Lasso and Dantzig Estimators
نویسندگان
چکیده
We consider the estimation of regression coefficients in a high-dimensional linear model. A lower bound of the minimax `q risk is provided for regression coefficients in `r balls, along with a minimax lower bound for the tail of the `q loss. Under certain conditions on the design matrix and penalty level, we prove that these minimax convergence rates are attained by both the Lasso and Dantzig estimators.
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