This paper provides some extended results on estimating parameter matrix of several regression models when the covariate or response possesses weaker moment condition. We study the $M$-estimator of Fan et al. (Ann Stat 49(3):1239--1266, 2021) for matrix completion model with $(1+\epsilon)$-th moment noise. The corresponding phase transition phenomenon is observed. When $1> \epsilon>0$, the robust estimator possesses a slower convergence rate compared with previous literature. For high dimensional multiple index coefficient model, we propose an improved estimator via applying the element-wise truncation method to handle heavy-tailed data with finite fourth moment. The extensive simulation study validates our theoretical results.
翻译:本文在估计若干回归模型的参数矩阵时,如果共变或反应具有较弱的时点条件,则提供一些关于估计数个回归模型参数矩阵的延伸结果。我们研究Fan et al. (AnnnStat 49(3):1239-1266, 2021) 的美元-美元-美元-美元-美元-秒噪音的矩阵完成模型。观察到相应的阶段过渡现象。当1美元> \ epsilon>0美元时,稳健的估测器与先前的文献相比,其趋同率较慢。对于高维多指数系数模型,我们建议通过应用元素智能脱钩法处理第四次有限时间的重尾数据来改进估计值。广泛的模拟研究证实了我们的理论结果。