Foundations of Optimum Experimental Design

the long version

This book contains an exposition of the theory and methods of optimum experimental design. It is aimed at giving an exact and systematic mathemati-cal presentation of a topic which is sufficiently evolved to be considered a self-contained part of mathematical statistics. The book will be useful as an introductory text for researchers in the field, as a textbook for students of statistics, and as a theoretical background for users of optimum design in experimental research: physics, chemistry, geodesy, building and electrical engineering, etc. After presenting the linear estimation theory necessary for understanding experimental design, the book moves on to a discussion of the uniform ordering of designs, admissable designs, and properties of the variances of estimates. Discontinuities which can appear with singular designs are ana-lysed here and in other parts of the book. Properties of optimality criteria are then presented, in particular the important consequences of convexity, e.g. the equivalence theorem, are discussed in detail. Methods of computations of optimum designs precede a chapter on generalization of the theory to in-finite-dimensional models.