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

AbstractIn a linear model Y = Xβ + Z a linear functional β → γ′β 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 J of all equivariant estimation functions and is admissible in the class E 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 J and also admissible in E only if Y is normally distributed