论文标题
高维推理与L1-Norm惩罚的异常值
High-dimensional inference robust to outliers with l1-norm penalization
论文作者
论文摘要
本文研究了具有离群值的高维线性回归模型的推论。稀疏性约束施加在协变量系数的载体上。离群值的数量可以随样本量而增长，而它们的比例为0。我们提出了一个两步程序，以推断回归器固定子集的系数。第一步是基于几个平方根Lasso L1-Norm惩罚估计器，而第二步是应用于选择精确回归的普通最小二乘估计器。我们建立了两步估计量的渐近正态性。从均匀性下，无异常值应用于模型时，提出的程序是有效的。这种方法在计算上也是有利的，相当于解决有限数量的凸优化程序。
This paper studies inference in the high-dimensional linear regression model with outliers. Sparsity constraints are imposed on the vector of coefficients of the covariates. The number of outliers can grow with the sample size while their proportion goes to 0. We propose a two-step procedure for inference on the coefficients of a fixed subset of regressors. The first step is a based on several square-root lasso l1-norm penalized estimators, while the second step is the ordinary least squares estimator applied to a well chosen regression. We establish asymptotic normality of the two-step estimator. The proposed procedure is efficient in the sense that it attains the semiparametric efficiency bound when applied to the model without outliers under homoscedasticity. This approach is also computationally advantageous, it amounts to solving a finite number of convex optimization programs.
