  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.
