Elfving’s theorem for R-optimality of experimental designs

The present paper is devoted to the construction of R-optimal designs in multiresponse linear models. The R-optimality criterion introduced by Dette (J R Stat Soc Ser B 59:97–110, 1997) minimizes the volume of Bonferroni rectangular confidence region for the parameter estimation. A generalization of Elfving’s theorem is proved for the optimal designs with respect to R-optimality, which gives a geometric characterization of R-optimal designs. The geometric characterizations of the R-optimal designs are illustrated by four examples.