Minimax estimation in linear regression with ellipsoidal constraints

In the paper we consider estimation of the regression coefficients in a linear regression model Y=Xβ+εY=Xβ+ε under ellipsoid constraints on the parameter space and the weighted squared error loss function. We prove that the minimax linear decision rule d*d* is also minimax when the class DD of possible estimators of the regression coefficients ββ is unrestricted. We derive that result assuming that the matrices AA and BB, which define the loss and the constraints, have the same eigenvectors as the matrix X′XX′X.