The Equivariance Criterion in a Linear Model for Fixed-X Cases

Abstract: 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.