Abstract: This paper proposes a new class of optimum design criteria for the linear regression model with responses based on the volume of the predictive ellipsoid. This is referred to as -optimality. The -optimality criterion is invariant with respect to different parameterizations of the model, and reduces to -optimality as proposed by Dette and O'brien (1999) in single response situations. An equivalence theorem for -optimality is provided and used to verify -optimality of designs, and this is illustrated by several examples.
Key words and phrases: General equivalence theorem, multiresponse linear models, optimal design, predictive ellipsoid.