Foundations of Optimum Experimental DesignIntroductory remarks about the experiment and its disign. The regression model and methods of estimation. The ordering of designs and the properties of variaces of estimates. Optimality critaria in the regression model. Iterative computation of optimum desings Design of experiments in particular cases. The functional model and measurements of physical fields. |
Contents
Introductory Remarks about the Experiment | 1 |
The Regression Model and Methods of Estimation | 15 |
The Ordering of Designs and the Properties | 47 |
Copyright | |
6 other sections not shown
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a₁ according to Eq According to Proposition BLUE-s Chapter II.2 compact set computing considered continuous convergence convex covariance matrix criterion function D-optimality D-optimum defined by Eq Denote diag diagonal eigenvalues eigenvectors equal experiment finite follows from Proposition function defined functional g g-inverse Hence Hilbert space implies inequality information matrix iterative methods iterative procedure linear estimate linear functional linear space lower semicontinuous M₁ mapping measure minimum nonlinear nonsingular nonsingular matrix o-algebra observations obtain optimality criteria optimum design ordering of designs orthonormal eigenvectors points polynomial positive definite positive semidefinite PROOF properties Proposition III.13 Proposition IV.28 Prove random variables regression model Schur's ordering sequence signed measure subset Suppose symmetric theorem trials unbiassed estimate v₁ vareg varɛg varg variance vector x₁ β)Μ₁ θεΘ ξεΞ ξη