This paper provides some extended results on estimating the parameter matrix of high-dimensional regression model when the covariate or response possess weaker moment condition. We investigate the $M$-estimator of Fan et al. (Ann Stat 49(3):1239--1266, 2021) for matrix completion model with $(1+\epsilon)$-th moments. The corresponding phase transition phenomenon is observed. When $\epsilon \geq 1$, the robust estimator possesses the same convergence rate as previous literature. While $1> \epsilon>0$, the rate will be slower. For high dimensional multiple index coefficient model, we also apply the element-wise truncation method to construct a robust estimator which handle missing and heavy-tailed data with finite fourth moment.

翻译：本文在估计高维回归模型的参数矩阵时,当共变或反应具有较弱的瞬时状态时,提供一些关于估算高维回归模型参数矩阵的延伸结果。我们调查Fan et al. (ANStat 49(3):1239-1266, 2021) 用于使用(1 ⁇ -epsilon) 秒数的矩阵完成模型(AnnStat 49(3):1239-1266, 2021) 。观察到相应的阶段过渡现象。当 $\epsilon\geq 1 美元时, 稳健的测算器拥有与先前文献相同的趋同率。 虽然$>\epsilon>0 美元, 速率会较慢。对于高维多指数系数模型, 我们还采用元素智能脱轨法来构建一个强的测算器, 该测算器在第四秒内处理缺失和重成型数据。