General ridge estimators are typical linear estimators in a general linear model. The class of them include some shrinkage estimators in addition to classical linear unbiased estimators such as the ordinary least squares estimator and the weighted least squares estimator. We derive necessary and sufficient conditions under which two typical general ridge estimators coincide. In particular, two noteworthy conditions are added to those from previous studies. The first condition is given as a seemingly column space relationship to the covariance matrix of the error term, and the second one is based on the biases of general ridge estimators. Another problem studied in this paper is to derive an equivalence condition such that equality between two residual sums of squares holds when general ridge estimators are considered.

翻译：广义岭估计量是一般线性模型中的典型线性估计量。该类估计量不仅包含经典线性无偏估计量（如普通最小二乘估计量和加权最小二乘估计量），还包含一些压缩估计量。本文推导了两个典型广义岭估计量相等的充分必要条件，特别在已有研究基础上补充了两个值得注意的条件：第一个条件表现为与误差项协方差矩阵的列空间关系，第二个条件基于广义岭估计量的偏差。本文研究的另一个问题是推导当采用广义岭估计量时，两个残差平方和相等的等价条件。