标题： 约束M估计量的几何观点 显示英文标题

标题： A Geometric View on Constrained M-Estimators

摘要： 我们研究约束M估计量的估计误差，并推导出由约束集的高斯宽度决定的期望估计误差的显式上界。 考虑了真实参数位于约束集边界上的情况（匹配约束）以及真实参数严格在约束集内部的情况（不匹配约束）。 对于这两种情况，我们推导了在规范链接函数的广义线性模型中回归问题的新通用估计误差界。 我们针对不匹配约束情况的误差界在其对样本量的依赖性方面对于Lasso的高斯线性回归是极小极大最优的。 显示英文摘要

摘要： We study the estimation error of constrained M-estimators, and derive explicit upper bounds on the expected estimation error determined by the Gaussian width of the constraint set. Both of the cases where the true parameter is on the boundary of the constraint set (matched constraint), and where the true parameter is strictly in the constraint set (mismatched constraint) are considered. For both cases, we derive novel universal estimation error bounds for regression in a generalized linear model with the canonical link function. Our error bound for the mismatched constraint case is minimax optimal in terms of its dependence on the sample size, for Gaussian linear regression by the Lasso.