Book ChapterDOI
Optimal Regression Designs
Bikas K. Sinha,Nripes Kumar Mandal,Manisha Pal,Premadhis Das +3 more
- Vol. 1028, pp 9-21
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TLDR
In this paper, the authors review the theory of optimum regression designs and introduce the concept of continuous design and different optimality criteria, including the role of de la Garza phenomenon and Loewner order domination.Abstract:
In this chapter, we review the theory of optimum regression designs. Concept of continuous design and different optimality criteria are introduced. The role of de la Garza phenomenon and Loewner order domination are discussed. Equivalence theorems for different optimality criteria, which play an important role in checking the optimality of a given otherwise prospective design, are presented. These results are repeatedly used in later chapters in the search for optimal mixture designs. We present standard optimality results for single variable polynomial regression model and multivariate linear and quadratic regression model . Kronecker product representation of the model(s) and related optimality results are also discussed.read more
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Journal ArticleDOI
Optimal Design of Blocked and Split-Plot Experiments for Fixed Effects and Variance Component Estimation
TL;DR: In this paper, a new Bayesian optimal design criterion is proposed which focuses on both the variance components and the fixed effects of blocked and split-plot response surface experiments and incorporates prior information about the variance component through log-normal or beta prior distributions.
References
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Journal ArticleDOI
An Analysis of Transformations
George E. P. Box,David Cox +1 more
TL;DR: In this article, Lindley et al. make the less restrictive assumption that such a normal, homoscedastic, linear model is appropriate after some suitable transformation has been applied to the y's.
Book ChapterDOI
On the Experimental Attainment of Optimum Conditions
George E. P. Box,K. B. Wilson +1 more
TL;DR: The work described in this article is the result of a study extending over the past few years by a chemist and a statistician, which has come about mainly in answer to problems of determining optimum conditions in chemical investigations, but they believe that the methods will be of value in other fields where experimentation is sequential and the error fairly small.
Book
Optimal Design of Experiments
TL;DR: 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 References Biographies Bibliography Index as discussed by the authors
Journal ArticleDOI
The Equivalence of Two Extremum Problems
J. Kiefer,J. Wolfowitz +1 more
TL;DR: In this article, the authors consider the problem of defining probability measures with finite support, i.e., measures that assign probability one to a set consisting of a finite number of points.