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 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。该类估计量除了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）外，还涵盖一些收缩估计量。我们推导了两个广义岭估计量重合的充分必要条件。特别地，我们在前人研究的基础上补充了两个值得注意的条件。第一个条件表示为与误差项协方差矩阵的看似列空间关系，第二个条件则基于广义岭估计量的偏差。本文研究的另一个问题是推导一个等价条件，使得在考虑广义岭估计量时，两个残差平方和之间的相等性成立。