Asymptotic properties of robust regression estimators are well known. However, it is not always clear what is the best strategy for confidence intervals and hypothesis testing when the sample size is not very large, since the distribution of residuals coming from robust estimates has unknown properties for small samples. In the present work we propose an analysis of various strategies for estimating the variance-covariance matrix of the S estimators at the variation of n and p, considering different ρ functions. An adaptive correction strategy is proposed. In addition to the simulation study, an example on a benchmark dataset is shown.

中文翻译：

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S 个稳健回归估计量的协方差矩阵

稳健回归估计量的渐近特性是众所周知的。然而，当样本量不是很大时，置信区间和假设检验的最佳策略并不总是很清楚，因为来自稳健估计的残差分布对于小样本具有未知特性。在目前的工作中，我们提出了一种分析各种策略，用于估计 S 估计量在n和p变化时的方差 - 协方差矩阵，同时考虑不同的ρ函数。提出了一种自适应校正策略。除了模拟研究之外，还显示了一个基准数据集的示例。