DS-optimal designs in one way ANOVA

Characterization and construction of optimal designs using the familiar optimality criteria, for example A-, D- and E-optimality are well studied in the literature. However the study of the Distance Optimality (DS-) criterion introduced by Sinha (1970) has very recently drawn attention of researchers. In the present article, we consider the singularly estimable full rank problem of estimating the full set of elementary treatment contrasts using the DS optimality criterion in the set up of a one way ANOVA model. Using a limit argument it turns out that a CRD in which difference between any two allocation numbers is at the most unity is uniquely DS-optimal. Acknowledgement. We are thankful to Prof. B. K. Sinha for suggesting the problem to us and many helpful discussions with him. We are also thankful to the referees for drawing our attention to the reference of Bischoff (1995) and many helpful comments.