E-optimum Designs in Linear Models with Both Qualitative and Quantitative Factors of Influence

In most experimental situations the outcome is influenced by various factors and different interaction structures. For a variety of simple but practically useful examples we investigate the generation of E-optimum designs, i. e. designs which minimize the maximum variance for all normalized estimates. 1 Introduction We consider situations in which the outcome of an experiment depends on two or more factors of influence. In particular, the response function associated with the experiment can be linearly parametrized, i. e. the observation Y (t) = P p i=1 a i (t)fi i + Z can be represented as a linear combination of the known regression functions a 1 ; :::; a p with unknown coefficients fi 1 ; :::; fi p , where t = (t 1 ; :::; t K ) 0 is the setting of the K factors of influence and Z denotes random noise. For N different experiments which can be realized according to the linear model Y n (t (n) ) = a(t (n) ) 0 fi +Z n the experimental condition t (n) 2 T can be chosen by ..