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E-raamat: Theory and Application of Uniform Experimental Designs

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  • Formaat: EPUB+DRM
  • Sari: Lecture Notes in Statistics 221
  • Ilmumisaeg: 02-Oct-2018
  • Kirjastus: Springer Verlag, Singapore
  • Keel: eng
  • ISBN-13: 9789811320415
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Theory and Application of Uniform Experimental DesignsSuurem pilt
  • Formaat: EPUB+DRM
  • Sari: Lecture Notes in Statistics 221
  • Ilmumisaeg: 02-Oct-2018
  • Kirjastus: Springer Verlag, Singapore
  • Keel: eng
  • ISBN-13: 9789811320415
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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.
1 Introduction
1(42)
1.1 Experiments
1(8)
1.1.1 Examples
2(3)
1.1.2 Experimental Characteristics
5(2)
1.1.3 Type of Experiments
7(2)
1.2 Basic Terminologies Used
9(3)
1.3 Statistical Models
12(14)
1.3.1 Factorial Designs and ANOVA Models
13(3)
1.3.2 Fractional Factorial Designs
16(3)
1.3.3 Linear Regression Models
19(4)
1.3.4 Nonparametric Regression Models
23(2)
1.3.5 Robustness of Regression Models
25(1)
1.4 Word-Length Pattern: Resolution and Minimum Aberration
26(6)
1.4.1 Ordering
26(1)
1.4.2 Defining Relation
27(2)
1.4.3 Word-Length Pattern and Resolution
29(1)
1.4.4 Minimum Aberration Criterion and Its Extension
30(2)
1.5 Implementation of Uniform Designs for Multifactor Experiments
32(5)
1.6 Applications of the Uniform Design
37(6)
Exercises
37(3)
References
40(3)
2 Uniformity Criteria
43(58)
2.1 Overall Mean Model
43(3)
2.2 Star Discrepancy
46(6)
2.2.1 Definition
46(2)
2.2.2 Properties
48(4)
2.3 Generalized L2-Discrepancy
52(12)
2.3.1 Definition
53(1)
2.3.2 Centered La -Discrepancy
54(2)
2.3.3 Wrap-around L2-Discrepancy
56(1)
2.3.4 Some Discussion on CD and WD
57(4)
2.3.5 Mixture Discrepancy
61(3)
2.4 Reproducing Kernel for Discrepancies
64(6)
2.5 Discrepancies for Finite Numbers of Levels
70(4)
2.5.1 Discrete Discrepancy
71(2)
2.5.2 Lee Discrepancy
73(1)
2.6 Lower Bounds of Discrepancies
74(27)
2.6.1 Lower Bounds of the Centered L2-Discrepancy
76(3)
2.6.2 Lower Bounds of the Wrap-around L2-Discrepancy
79(7)
2.6.3 Lower Bounds of Mixture Discrepancy
86(5)
2.6.4 Lower Bounds of Discrete Discrepancy
91(3)
2.6.5 Lower Bounds of Lee Discrepancy
94(3)
Exercises
97(2)
References
99(2)
3 Construction of Uniform Designs---Deterministic Methods
101(54)
3.1 Uniform Design Tables
102(7)
3.1.1 Background of Uniform Design Tables
102(5)
3.1.2 One-Factor Uniform Designs
107(2)
3.2 Uniform Designs with Multiple Factors
109(6)
3.2.1 Complexity of the Construction
109(1)
3.2.2 Remarks
110(5)
3.3 Good Lattice Point Method and Its Modifications
115(7)
3.3.1 Good Lattice Point Method
115(2)
3.3.2 The Leave-One-Out glpm
117(4)
3.3.3 Good Lattice Point with Power Generator
121(1)
3.4 The Cutting Method
122(2)
3.5 Linear Level Permutation Method
124(5)
3.6 Combinatorial Construction Methods
129(26)
3.6.1 Connection Between Uniform Designs and Uniformly Resolvable Designs
129(4)
3.6.2 Construction Approaches via Combinatorics
133(12)
3.6.3 Construction Approach via Saturated Orthogonal Arrays
145(2)
3.6.4 Further Results
147(2)
Exercises
149(3)
References
152(3)
4 Construction of Uniform Designs---Algorithmic Optimization Methods
155(28)
4.1 Numerical Search for Uniform Designs
155(3)
4.2 Threshold-Accepting Method
158(8)
4.3 Construction Method Based on Quadratic Form
166(17)
4.3.1 Quadratic Forms of Discrepancies
167(1)
4.3.2 Complementary Design Theory
168(4)
4.3.3 Optimal Frequency Vector
172(5)
4.3.4 Integer Programming Problem Method
177(2)
Exercises
179(1)
References
180(3)
5 Modeling Techniques
183(26)
5.1 Basis Functions
184(7)
5.1.1 Polynomial Regression Models
184(4)
5.1.2 Spline Basis
188(1)
5.1.3 Wavelets Basis
189(1)
5.1.4 Radial Basis Functions
190(1)
5.1.5 Selection of Variables
191(1)
5.2 Modeling Techniques: Kriging Models
191(9)
5.2.1 Models
192(2)
5.2.2 Estimation
194(1)
5.2.3 Maximum Likelihood Estimation
195(1)
5.2.4 Parametric Empirical Kriging
196(1)
5.2.5 Examples and Discussion
197(3)
5.3 A Case Study on Environmental Data---Model Selection
200(9)
Exercises
205(2)
References
207(2)
6 Connections Between Uniformity and Other Design Criteria
209(34)
6.1 Uniformity and Isomorphism
209(5)
6.2 Uniformity and Orthogonality
214(4)
6.3 Uniformity and Confounding
218(3)
6.4 Uniformity and Aberration
221(7)
6.5 Projection Uniformity and Related Criteria
228(4)
6.5.1 Projection Discrepancy Pattern and Related Criteria
228(3)
6.5.2 Uniformity Pattern and Related Criteria
231(1)
6.6 Majorization Framework
232(11)
6.6.1 Based on Pairwise Coincidence Vector
232(2)
6.6.2 Minimum Aberration Majorization
234(4)
Exercises
238(1)
References
239(4)
7 Applications of Uniformity in Other Design Types
243(20)
7.1 Uniformity in Block Designs
243(4)
7.1.1 Uniformity in BIBDs
243(1)
7.1.2 Uniformity in PRIBDs
244(1)
7.1.3 Uniformity in POTBs
245(2)
7.2 Uniformity in Supersaturated Designs
247(3)
7.2.1 Uniformity in Two-Level SSDs
248(1)
7.2.2 Uniformity in Mixed-Level SSDs
249(1)
7.3 Uniformity in Sliced Latin Hypercube Designs
250(5)
7.3.1 A Combined Uniformity Measure
251(1)
7.3.2 Optimization Algorithms
252(1)
7.3.3 Determination of the Weight ω
253(2)
7.4 Uniformity Under Errors in the Level Values
255(8)
Exercises
258(2)
References
260(3)
8 Uniform Design for Experiments with Mixtures
263(34)
8.1 Introduction to Design with Mixture
263(7)
8.1.1 Some Types of Designs with Mixtures
265(3)
8.1.2 Criteria for Designs with Mixtures
268(2)
8.2 Uniform Designs of Experiments with Mixtures
270(15)
8.2.1 Discrepancy for Designs with Mixtures
270(3)
8.2.2 Construction Methods for Uniform Mixture Design
273(3)
8.2.3 Uniform Design with Restricted Mixtures
276(4)
8.2.4 Uniform Design on Irregular region
280(5)
8.3 Modeling Technique for Designs with Mixtures
285(12)
Exercises
292(3)
References
295(2)
Subject Index 297
Kai-Tai Fang is a professor at the BNU-HKBU United International college and is a research professor at the Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, China.





Min-Qian Liu is a professor at the Institute of Statistics, Nankai University, Tianjin, China





Hong Qin is a professor at the Faculty of Mathematics and Statistics, Central China Normal





University, Wuhan, China





Yong-Dao Zhou is a professor at the Institute of Statistics, Nankai University, Tianjin, China
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