Some General Points in the Theory of Optimal Experimental Design

Summary This paper is an expansion of comments made by the author in the discussion following the reading of papers by Laycock (1972) and Wynn (1972). Section 2 presents a direct proof and interpretation of the equivalence theorem for the general case of a concave criterion function. This has implications for iterative algorithms of the type suggested by Wynn, as indicated in Section 3. Section 4 is concerned with a characterization of D,-optimality as a criterion which preserves ranking of designs under certain transformations of the problem. Section 5 discusses quasi-linear representations of the criterion for c-optimality.