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
Common terms and phrases
according to Eq According to Proposition B₁ BLUE-s Chapter compact set computing considered continuous convergence convex covariance matrix criterion function D-optimality D-optimum defined by Eq Denote diag diagonal eigenvalues eigenvectors equal equivalent experiment Experimental Design finite follows from Proposition function defined functional g g-inverse Hence Hilbert space implies inequality information matrix iterative methods iterative procedure l₁ linear estimate linear functional linear space lower semicontinuous M₁ mapping mathematics measure MɛM minimum nonlinear nonsingular nonsingular matrix observations obtain optimality criteria optimum design ordering of designs orthonormal eigenvectors Pázman points polynomial positive definite positive semidefinite PROOF properties Proposition III.14 Proposition IV.28 Prove random variables regression model Schur's ordering sequence signed measure Statist subset Suppose symmetric theorem trials u₁ unbiassed estimate vareg varg variance vector