THE ROLE OF SYMMETRY AND APPROXIMATION IN EXACT DESIGN OPTIMALITY

Publisher Summary This chapter explores the role of symmetry and approximation in exact design optimality. It also reviews functionals of the expected squared errors and, although the results pertain also to certain settings where biased estimators are called for, the chapter focuses only on unbiased estimators. In the approximate theory, if a compact group G operates appropriately on (*, f, ς, Φ), which includes convexity in ξ of some increasing function of ΦM(ξ), then there is an approximate Φ-optimum in ξ, which is G-invariant for all g in G and measurable. This chapter describes the relation of approximate to exact theory.