The optimal design problem for the estimation of several linear combinations is considered in the usual linear regression model . An optimal design minimizes a (weighted) p-norm of the variances of the least squares estimates for the different linear combinations. A generalized Elfving theorem is used to derive the relation of the new optimality criterion to the E-optimal design problem. It is shown that the E-optimal design for the parameter minimizes such a (weighted) p-norm whenever the vector is an inball vector of a symmetric convex and compact ‘Elfving set’ in .
