Optimal Design of Experiments

  title={Optimal Design of Experiments},
  author={Friedrich Pukelsheim},
Experimental Designs in Linear Models Optimal Designs for Scalar Parameter Systems Information Matrices Loewner Optimality Real Optimality Criteria Matrix Means The General Equivalence Theorem Optimal Moment Matrices and Optimal Designs D-, A-, E-, T-Optimality Admissibility of Moment and Information Matrices Bayes Designs and Discrimination Designs Efficient Designs for Finite Sample Sizes Invariant Design Problems Kiefer Optimality Rotatability and Response Surface Designs Comments and… 
Optimal repeated measurements designs: the linear optimality equations
In approximate design theory, necessary and sufficient conditions that a repeated measurements design be universally optimal are given as linear equations whose unknowns are the proportions of
D-optimal minimax regression designs on discrete design space
One classical design criterion is to minimize the determinant of the covariance matrix of the regression estimates, and the designs are called D-optimal designs. To reflect the nature that the
Asymptotic optimal designs under long-range dependence error structure
We discuss the optimal design problem in regression models with long range dependence error structure. Asymptotic optimal designs are derived and it is demonstrated that these designs depend only
Optimal Designs for Regression Models With a Constant Coefficient of Variation
In this article we consider the problem of constructing optimal designs for models with a constant coefficient of variation. We explore the special structure of the information matrix in these models
26 Optimal design: Exact theory
  • Ching-Shui Cheng
  • Mathematics, Computer Science
    Design and analysis of experiments
  • 1996
Publisher Summary This chapter presents an introduction to the exact theory of optimal design. It presents several useful techniques that are used in the application of block designs, row–column
Optimal Designs for Additive Linear Models
In additive linearr models optimal designs can be constructed as a product of those marginal designs which have certain optimality properties in the corresponding single-factor models. In particular,
Optimal Regression Designs in Symmetric Domains
Model(s): Fixed coefficient regression models Single factor polynomial Multi-factor linear Symmetric experimental domains: Interval, hypercube and unit ball Major tools: de la Garza (DLG)
D-optimal minimax design criterion for two-level fractional factorial designs
A D-optimal minimax design criterion is proposed to construct two-level fractional factorial designs, which can be used to estimate a linear model with main effects and some specified interactions.
General weighted optimality of designed experiments
The standard approach to finding optimal experimental designs employs conventional measures of design efficacy, such as the $A$, $E$, and $D$-criterion, that assume equal interest in all estimable
Optimal Euclidean Design
The main problem in optimal design theory is to find a finite set of observation points (design), where unknown parameters of a regression model are “well-estimated” with some statistical criterion.


Optimum Experimental Designs
This book discusses experiments with both qualitative and quantitative factors, and the choice of a model and criteria for a good experiment, as well as the analysis of experiments.
The equivalence of two extremum problems
Let f 1 , …, f k be linearly independent real functions on a space X , such that the range R of (f 1 , …, f k ) is a compact set in k dimensional Euclidean space. (This will happen, for example, if