In this article, we explored the usage of the equivariance criterion in linear model with fixed-X for the estimation and extended the model to allow multiple populations, which, in turn, leads to a larger transformation group. The minimum risk equivariant estimators of the coefficient vector and the covariance matrix were derived via the maximal invariants, which was consistent with earlier works. This article serves as an early exploration of the equivariance criterion in linear model.

翻译：本文探讨了等变性准则在固定X线性模型估计中的应用，并将该模型扩展至允许多个总体，从而引出了更大的变换群。通过极大不变量，我们推导出了系数向量与协方差矩阵的最小风险等变估计量，这与早期研究结果一致。本文是对线性模型中等变性准则的初步探索。