Robust estimators are often lacking a closed-form expression for the computation of their residual covariance matrix. In fact, it is also a prerequisite to obtain critical values for normalized residuals. We present an approach based on Monte Carlo simulation to compute the residual covariance matrix and critical values for robust estimators. Although initially designed for robust estimators, the new approach can be extended for other adjustment procedures. In this sense, the proposal was applied to both well-known minimum L1-norm and least squares into three different leveling network geometries. The results show that (1) the covariance matrix of residuals changes along with the estimator; (2) critical values for minimum L1-norm based on a false positive rate cannot be derived from well-known test distributions; (3) in contrast to critical values for extreme normalized residuals in least squares, critical values for minimum L1-norm do not necessarily tend to be higher as network redundancy increases.

中文翻译：

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最小L1范数中残差和临界值的基于蒙特卡罗的协方差矩阵

稳健估计器通常缺乏用于计算其残差协方差矩阵的封闭形式表达式。事实上，获得归一化残差的临界值也是一个先决条件。我们提出了一种基于蒙特卡罗模拟的方法来计算鲁棒估计器的残差协方差矩阵和临界值。尽管最初是为稳健估计器设计的，但新方法可以扩展到其他调整程序。从这个意义上说，该提议被应用于众所周知的最小 L1 范数和最小二乘法到三个不同的调平网络几何结构中。结果表明：（1）残差的协方差矩阵随着估计量的变化而变化；(2) 基于误报率的最小 L1 范数的临界值不能从众所周知的测试分布中导出；