In the Gauss–Markov model, this paper derives a necessary and sufficient condition under which two general ridge estimators coincide with each other. The condition is given as a structure of the dispersion matrix of the error term. Since the class of estimators considered here contains linear unbiased estimators such as the ordinary least squares estimator and the best linear unbiased estimator, our result can be viewed as a generalization of the well known theorems on the equality between these two estimators, which have been fully studied in the literature. Two related problems are also considered: equality between two residual sums of squares, and classification of dispersion matrices by a perturbation approach.

中文翻译：

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与两个一般脊估计量之间的等式相关联的协方差结构

在高斯-马尔可夫模型中，本文推导出两个一般脊估计量相互重合的充分必要条件。该条件作为误差项的色散矩阵的结构给出。由于这里考虑的估计量类别包含线性无偏估计量，例如普通最小二乘估计量和最佳线性无偏估计量，我们的结果可以看作是对这两个估计量之间的等式的众所周知的定理的推广，这些定理已经完全在文献中研究过。还考虑了两个相关问题：两个残差平方和之间的相等性，以及通过扰动方法对色散矩阵进行分类。