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" Theory and application of uniform experimental designs / "
Kai-Tai Fang, Min-Qian Liu, Hong Qin, Yong-Dao Zhou.
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BL
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| Record Number
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890078
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| Main Entry
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Fang, Kaitai
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| Title & Author
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Theory and application of uniform experimental designs /\ Kai-Tai Fang, Min-Qian Liu, Hong Qin, Yong-Dao Zhou.
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| Publication Statement
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Singapore :: Springer,, 2018.
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| Series Statement
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Lecture notes in statistics,; volume 221
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| Page. NO
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1 online resource (xvi, 300 pages) :: illustrations (some color)
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| ISBN
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9789811320415
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: 9789811320422
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: 9811320411
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: 981132042X
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9789811320408
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9811320403
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Intro; Foreword; Preface; References; Contents; 1 Introduction; 1.1 Experiments; 1.1.1 Examples; 1.1.2 Experimental Characteristics; 1.1.3 Type of Experiments; 1.2 Basic Terminologies Used; 1.3 Statistical Models; 1.3.1 Factorial Designs and ANOVA Models; 1.3.2 Fractional Factorial Designs; 1.3.3 Linear Regression Models; 1.3.4 Nonparametric Regression Models; 1.3.5 Robustness of Regression Models; 1.4 Word-Length Pattern: Resolution and Minimum Aberration; 1.4.1 Ordering; 1.4.2 Defining Relation; 1.4.3 Word-Length Pattern and Resolution; 1.4.4 Minimum Aberration Criterion and Its Extension.
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1.5 Implementation of Uniform Designs for Multifactor Experiments1.6 Applications of the Uniform Design; References; 2 Uniformity Criteria; 2.1 Overall Mean Model; 2.2 Star Discrepancy; 2.2.1 Definition; 2.2.2 Properties; 2.3 Generalized L2-Discrepancy; 2.3.1 Definition; 2.3.2 Centered L2-Discrepancy; 2.3.3 Wrap-around L2-Discrepancy; 2.3.4 Some Discussion on CD and WD; 2.3.5 Mixture Discrepancy; 2.4 Reproducing Kernel for Discrepancies; 2.5 Discrepancies for Finite Numbers of Levels; 2.5.1 Discrete Discrepancy; 2.5.2 Lee Discrepancy; 2.6 Lower Bounds of Discrepancies.
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2.6.1 Lower Bounds of the Centered L2-Discrepancy2.6.2 Lower Bounds of the Wrap-around L2-Discrepancy; 2.6.3 Lower Bounds of Mixture Discrepancy; 2.6.4 Lower Bounds of Discrete Discrepancy; 2.6.5 Lower Bounds of Lee Discrepancy; References; 3 Construction of Uniform Designs-Deterministic Methods; 3.1 Uniform Design Tables; 3.1.1 Background of Uniform Design Tables; 3.1.2 One-Factor Uniform Designs; 3.2 Uniform Designs with Multiple Factors; 3.2.1 Complexity of the Construction; 3.2.2 Remarks; 3.3 Good Lattice Point Method and Its Modifications; 3.3.1 Good Lattice Point Method.
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3.3.2 The Leave-One-Out glpm3.3.3 Good Lattice Point with Power Generator; 3.4 The Cutting Method; 3.5 Linear Level Permutation Method; 3.6 Combinatorial Construction Methods; 3.6.1 Connection Between Uniform Designs and Uniformly Resolvable Designs; 3.6.2 Construction Approaches via Combinatorics; 3.6.3 Construction Approach via Saturated Orthogonal Arrays; 3.6.4 Further Results; References; 4 Construction of Uniform Designs-Algorithmic Optimization Methods; 4.1 Numerical Search for Uniform Designs; 4.2 Threshold-Accepting Method; 4.3 Construction Method Based on Quadratic Form.
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4.3.1 Quadratic Forms of Discrepancies4.3.2 Complementary Design Theory; 4.3.3 Optimal Frequency Vector; 4.3.4 Integer Programming Problem Method; References; 5 Modeling Techniques; 5.1 Basis Functions; 5.1.1 Polynomial Regression Models; 5.1.2 Spline Basis; 5.1.3 Wavelets Basis; 5.1.4 Radial Basis Functions; 5.1.5 Selection of Variables; 5.2 Modeling Techniques: Kriging Models; 5.2.1 Models; 5.2.2 Estimation; 5.2.3 Maximum Likelihood Estimation; 5.2.4 Parametric Empirical Kriging; 5.2.5 Examples and Discussion; 5.3 A Case Study on Environmental Data-Model Selection; References.
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| Abstract
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The book provides necessary knowledge for readers interested in developing the theory of uniform experimental design. It discusses measures of uniformity, various construction methods of uniform designs, modeling techniques, design and modeling for experiments with mixtures, and the usefulness of the uniformity in block, factorial and supersaturated designs. Experimental design is an important branch of statistics with a long history, and is extremely useful in multi-factor experiments. Involving rich methodologies and various designs, it has played a key role in industry, technology, sciences and various other fields. A design that chooses experimental points uniformly scattered on the domain is known as uniform experimental design, and uniform experimental design can be regarded as a fractional factorial design with model uncertainty, a space-filling design for computer experiments, a robust design against the model specification, and a supersaturated design and can be applied to experiments with mixtures.
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| Subject
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Experimental design.
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Experimental design.
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| Subject
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Mathematics-- Probability Statistics-- General.
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Probability statistics.
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| Dewey Classification
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519.5/7
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| LC Classification
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QA279
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| Added Entry
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Liu, Min-Qian
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Qin, Hong
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Zhou, Yong-Dao
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