论文标题
高维度的稳健和稀疏的多项式回归
Robust and Sparse Multinomial Regression in High Dimensions
论文作者
论文摘要
为高维数据提出了多项式回归的稳健且稀疏的估计器。估计器的鲁棒性是通过修剪观测值来实现的，估计器的稀疏性是通过弹性净罚款获得的，弹性净罚款是$ l_1 $和$ l_2 $罚款的混合物。从这个角度来看，提出的估计器是ENET-LTS估算器\ Citep {Kurnaz18}的扩展，用于线性和逻辑回归到多项式回归设置。在引入计算算法后，进行了一项模拟研究，以显示与多项式回归估计量的非舒适版本相比的性能。一些真实的数据示例强调了此强大的估计器的有用性。
A robust and sparse estimator for multinomial regression is proposed for high dimensional data. Robustness of the estimator is achieved by trimming the observations, and sparsity of the estimator is obtained by the elastic net penalty, which is a mixture of $L_1$ and $L_2$ penalties. From this point of view, the proposed estimator is an extension of the enet-LTS estimator \citep{Kurnaz18} for linear and logistic regression to the multinomial regression setting. After introducing an algorithm for its computation, a simulation study is conducted to show the performance in comparison to the non-robust version of the multinomial regression estimator. Some real data examples underline the usefulness of this robust estimator.
