ABSTRACT

In Chapters 3 and 4, the construction of fixed-point or discrete designs for estimating the parameters in first- and second-order polynomial models, respectively, was presented. In Chapter 6, additional suggestions were made regarding the spread of the design points for minimizing the separate properties, variance of Y ^ ( x ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203740774/db1c32b9-4753-419f-abc0-35d0b2857016/content/inq12_431_1.tif"/> and the bias in Y ^ ( x ) , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203740774/db1c32b9-4753-419f-abc0-35d0b2857016/content/inq12_431_2.tif"/> , across the experimental region of interest. And while we have concentrated primarily on the integrated mean squared error of Y ^ ( x ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203740774/db1c32b9-4753-419f-abc0-35d0b2857016/content/inq12_431_3.tif"/> as the major criterion for choosing a design, we would be remiss in our role as authors if we did not at least acknowledge other design criteria, in particular, criteria based on the theory of design optimality and design robustness. These criteria are described in Sections 12.2–12.4. In addition, several measures of rotatability are discussed in Section 12.5. Finally, some comments concerning future research directions are given in Section 12.6.