Normal distribution assumption and least squares estimation function in the model of polynomial regression

In a linear model Y = X[beta] + Z a linear functional [beta] --> [gamma]'[beta] is to be estimated under squared error loss. It is well known that, provided Y is normally distributed, the ordinary least squares estimation function minimizes the risk uniformly in the class of all equivariant estimation functions and is admissible in the class of all unbiased estimation functions. For the design matrix X of a polynomial regression set up it is shown for almost all estimation problems that the ordinary least squares estimation function is uniformly best in and also admissible in only if Y is normally distributed.