Optimal Design of Experiments offers a rare blend of linear algebra, convex analysis, and statistics. The optimal design for statistical experiments is first formulated as a concave matrix optimization problem. Using tools from convex analysis, the problem is solved generally for a wide class of optimality criteria such as D-, A-, or E-optimality. The book then offers a complementary approach that calls for the study of the symmetry properties of the design problem, exploiting such notions as matrix majorization and the Kiefer matrix ordering. The results are illustrated with optimal designs for polynomial fit models, Bayes designs, balanced incomplete block designs, exchangeable designs on the cube, rotatable designs on the sphere, and many other examples.
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Book Description
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Book Description
Optimal Design of Experiments offers a rare blend of linear algebra, convex analysis, and statistics. Since the book's initial publication in 1993, readers have used its methods to derive optimal designs on the circle, optimal mixture designs, and optimal designs in other statistical models.
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Devoted to a unified optimality theory, merging three otherwise distinct mathematical disciplines to embrace an astonishingly wide variety of design problems. Outlines typical settings, namely D-, A-, and E-optimal, polynominal regression designs, Bayesian designs, structures for model discrimination, balanced incomplete block arrangements or rotatable response surface designs. The design problems stem from statistics but are solved using special tools from linear algebra and convex analysis.
--This text refers to an out of print or unavailable edition of this title.
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Inside This Book
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First Sentence:
This chapter provides an introduction to experimental designs for linear models. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
General Equivalence Theorem, Gauss-Markov Theorem, Elfving Theorem, Kiefer-Wolfowitz Theorem, Subgradient Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This chapter provides an introduction to experimental designs for linear models. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
General Equivalence Theorem, Gauss-Markov Theorem, Elfving Theorem, Kiefer-Wolfowitz Theorem, Subgradient Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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This book cites 81
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37
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- Ordinary Differential Equations (Classics in Applied Mathematics) by George F. Carrier in Front Matter (1), and Front Matter (2)
- Linear Models (Wiley Classics Library) by Shayle R. Searle on page 408, and Back Matter
- Statistical Inference by Clifford Springer in Back Matter (1), and Back Matter (2)
- Mathematical Statistics by Steven F. Arnold in Back Matter
- Differential Equations by HABERMAN in Front Matter
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- Advances in Stochastic Simulation Methods by N. Balakrishnan on page 132, page 187, and page 203
- mODa 7 - Advances in Model-Oriented Design and Analysis: Proceedings of the 7th International Workshop on Model-Oriented Design and Analysis held in ... 14-18, 2004 (Contributions to Statistics) by Alessandro Di Bucchianico on page 115, and page 199
- Optimum Design 2000 (Nonconvex Optimization and Its Applications (closed)) by Anthony Atkinson on page 14, and Back Matter
- Contemporary Multivariate Analysis And Design of Experiments (Series in Biostatistics) by Jianqing Fan on page 203
- Block Designs: A Randomization Approach: Volume II: Design (Lecture Notes in Statistics) by Tadeusz Calinski in Back Matter
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