Results in the Theory and Construction of D-Optimum Experimental Designs

Summary A method of generating D-optimum design measures as defined by Kiefer and Wolfowitz is briefly described. The relevant theorem is generalized to yield a method of generating D8-optimum design measures for a specific subset of s of the parameters in the regression model. The one parameter case is described in further detail. An analogous theorem for discrete designs with a fixed number of points is proved giving a lower bound to the optimality achievable with such designs. A final section is devoted to the loss in efficiency entailed by almost equal replication of a given discrete design. The discussion is extended to the one-dimensional polynomial model and the optimality of the replication is conjectured for the general case and proved for the quadratic case.