Model-Oriented Design of Experiments

Dr. Peter Hackl ist Professor für Statistik an der Wirtschaftsuniversität Wien und seit Dezember 2004 fachstatistischer Generaldirektor der Bundesanstalt Statistik Österreich.

These lecture notes are based on the theory of experimental design for courses given by Valerii Fedorov at a number of places, most recently at the University of Minnesota, the Vienna of University, and the University of Economics and Business Administra tion in Vienna. It was Peter Hackl's idea to publish these lecture notes and he took the lead in preparing and developing the text. The work continued longer than we expected, and we realized that a few thousand miles distance remains a serious hurdle even in the age of Internet and many electronic gadgets. While we mainly target graduate students in statistics, the book demands only a moderate background in calculus, matrix algebra and statistics. These are, to our knowledge, provided by almost any school in business and economics, natural sciences, or engineering. Therefore, we hope that the material may be easily understood by a relatively broad readership. The book does not try to teach recipes for the construction of experimental de signs. It rather aims at creating some understanding - and interest - in the problems and basic ideas of the theory of experimental design. Over the years, quite a number of books have been published on that subject with a varying degree of specialization. This book is organized in four chapters that layout in a rather compact form all.

Experimental design is an area of interested to statisticians working in many applied areas. This monograph by two of the leading researchers in the area discussed the optimal design of experiments. It assumes only a moderate background in calculus and statistics, and will of of interest to graduate students and researchers.

1 Some Facts From Regression Analysis.- 1.1 The Linear Model.- 1.2 More about the Information Matrix.- 1.3 Generalized Versions of the Linear Regression Model.- 1.4 Nonlinear Models.- 2 Convex Design Theory.- 2.1 Optimality Criteria.- 2.2 Some Properties of Optimality Criteria.- 2.3 Continuous Optimal Designs.- 2.4 The Sensitivity Function and Equivalence Theorems.- 2.5 Some Examples.- 2.6 Complements.- 3 Numerical Techniques.- 3.1 First Order Algorithm:D-criterion.- 3.2 First Order Algorithm: The General Case.- 3.3 Finite Sample Size.- 4 Optimal Design under Constraints.- 4.1 Cost Constraints.- 4.2 Constraints for Auxiliary Criteria.- 4.3 Directly Constrained Design Measures.- 5 Special Cases and Applications.- 5.1 Designs for Time-Dependent Models.- 5.2 Regression Models with Random Parameters.- 5.3 Mixed Models and Correlated Observations.- 5.4 Design for "Contaminated" Models.- 5.5 Model Discrimination.- 5.6 Nonlinear Regression.- 5.7 Design in Functional. Spaces.- A Some Results from Matrix Algebra.- B List of Symbols.- References.