Given prior information, on the regression parameters in form of inequalities a_i≦β_ib_i (all i) the resulting cuboid may be included in a certain ellipsoid. Using the weaker information β is contained in the ellipsoid' enables to derive a minimax linear estimator (MILE) of β.

If the interval lengths of the cuboid are fixed but the centre is moved then the MILE changes without its minimax risk being changed. Thus by a simulation experiment we are led to the,dependence of the numerical values of the MILE on the ellipsoid's centre. If the model is fitted properly and/cr if the ellipsoid's centre is nearly the unrestricted OLSE then the gain in efficiency coused by MILE is negligible.