Robust estimation in the errors-in-variables (EIV) model remains a difficult problem because of the leverage point and the masking effect and swamping effect. In this contribution, a new robust estimator is introduced for the EIV model. This method is a follow-up to least trimmed squares, which is applied to the Gauss–Markov model when only the observation vector contains outliers. We call this estimator the total least trimmed squares (TLTS) estimator because its criterion function consists of squared orthogonal residuals. The TLTS estimator excludes some large squared orthogonal residuals from the criterion function, thereby allowing the fit to ignore outliers. The TLTS estimator inherits appropriate equivariance properties, namely regression equivariance, scale equivariance and affine equivariance, and the maximal 50% asymptotic breakdown point in terms of observations y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \varvec{y} $$\end{document} within the special cofactor matrix structure. The TLTS estimate can directly be obtained by the exhaustive evaluation method. We further develop another algorithm for the TLTS estimator based on the branch-and-bound method without exhaustive evaluation, but the cofactor matrix of the independent variables needs to have a certain block structure. Finally, two simulation studies provide insights into the robustness and efficiency of the proposed algorithms.

中文翻译：

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用于计算总最小修整平方估计量的 BAB 算法

由于杠杆点以及掩蔽效应和沼泽效应，变量误差 (EIV) 模型中的稳健估计仍然是一个难题。在这个贡献中，为 EIV 模型引入了一个新的稳健估计器。这种方法是最小修整平方的后续方法，当只有观察向量包含异常值时，它被应用于高斯-马尔可夫模型。我们称这个估计器为总最小修整平方 (TLTS) 估计器，因为它的标准函数由平方正交残差组成。TLTS 估计器从标准函数中排除了一些大的平方正交残差，从而允许拟合忽略异常值。TLTS 估计量继承了适当的等方差属性，即回归等方差、尺度等方差和仿射等方差，y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs } \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \varvec{y} $$\end{document} 在特殊的辅因子矩阵结构中。TLTS估计可以通过穷举评估方法直接获得。我们进一步开发了另一种基于分支定界法的 TLTS 估计器算法，没有穷举评估，但自变量的辅因子矩阵需要具有一定的块结构。最后，两项模拟研究提供了对所提出算法的鲁棒性和效率的见解。