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.
翻译:对于高维数据,建议为多位回归建议一个稳健和稀有的估算值。 估计值的强度是通过对观测进行精减来实现的, 估计值的宽度则通过弹性网罚款获得, 弹性网罚款是1美元和2美元的混合罚款。 从这一点看, 提议的估算值是 enet- LTS 测量值 \ citep{Kurnaz18} 的延伸, 用于线性和后勤性回归到多位回归设置 。 在引入计算算法后, 进行模拟研究, 以显示与多位回归估量器的非紫外版相比的性能。 一些真实数据例子强调了这个强健的估量器的有用性 。