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El. knyga: Theory of Factorial Design: Single- and Multi-Stratum Experiments

  • Formatas: 409 pages
  • Išleidimo metai: 19-Apr-2016
  • Leidėjas: CRC Press Inc
  • Kalba: eng
  • ISBN-13: 9781466505582
Kitos knygos pagal šią temą:
Theory of Factorial Design: Single- and Multi-Stratum ExperimentsDidesnis paveikslėlis
  • Formatas: 409 pages
  • Išleidimo metai: 19-Apr-2016
  • Leidėjas: CRC Press Inc
  • Kalba: eng
  • ISBN-13: 9781466505582
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Cheng presents a rigorous and systematic treatment of the theoretical aspects of factorial design, incorporating the significant changes in the theory since the beginning of the 21st century. He minimizes the mathematics needed, and does not present the theory in its most general form, but lays the groundwork for learning it later. The book can serve as a reference for researchers or a textbook for graduate students who have taken a first course in the design of experiments and are familiar with linear algebra. Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

Bringing together both new and old results, Theory of Factorial Design: Single- and Multi-Stratum Experiments provides a rigorous, systematic, and up-to-date treatment of the theoretical aspects of factorial design. To prepare readers for a general theory, the author first presents a unified treatment of several simple designs, including completely randomized designs, block designs, and row-column designs. As such, the book is accessible to readers with minimal exposure to experimental design. With exercises and numerous examples, it is suitable as a reference for researchers and as a textbook for advanced graduate students.

In addition to traditional topics and a thorough discussion of the popular minimum aberration criterion, the book covers many topics and new results not found in existing books. These include results on the structures of two-level resolution IV designs, methods for constructing such designs beyond the familiar foldover method, the extension of minimum aberration to nonregular designs, the equivalence of generalized minimum aberration and minimum moment aberration, a Bayesian approach, and some results on nonregular designs. The book also presents a theory that provides a unifying framework for the design and analysis of factorial experiments with multiple strata (error terms) arising from complicated structures of the experimental units. This theory can be systematically applied to various structures of experimental units instead of treating each on a case-by-case basis.

Recenzijos

"The field of experimental design aims to help practitioners collect their data in a more efficient manner, or more specifically, run their experiments more effectively. There are many good textbooks in this area: the classical ones of the early 50's (e.g.,Cochran and Cox 1957) focused more on agricultural experimentation; the later ones of the late 70's (e.g., Box, Hunter, and Hunter 1978) focused more on industrial experimentation, and the recent ones (e.g., Santner, Williams, and Notz 2003; Fang, Li, and Sudjianto 2006) focused more on computer experiments. There are also some theoretical approaches, notably on optimal design (e.g., Pukelsheim 1993) and combinatorics (e.g., Street and Street 1987). This book is clearly one of the very first about design of experiment from a multi-stratum approach... Some topics have never appeared in any other book and the author has produced elegant mathematics accompanied with lucid explanations...I believe that this excellent book will soon become a must read for researchers and educators in experimental design. It could serve as a great reference or textbook for a high-level design course." -Dennis Lin, Penn State University, in Journal of the American Statistical Association, Volume 111, 2016 "... the book is extremely well written. It is a book on design theory authored by a well-known researcher in the field. As is pointed out by the author, the book provides an elegant and general theory, which once understood is simple to use and can be applied to various structures of experimental units in a unified and systematic way. The book is certainly a necessary reference for Technometrics readers who have an interest in the theory of factorial designs for single- and multi-stratum experiments." -Technometrics, May 2015 "This is a great book on factorial designs, both for academic statisticians and for practitioners. ... The style of the presentation, based on the discussion of a large number of real-life examples, supports the overall clarity and readability of the text. ... many chapters also contain some interesting topics usually not reported in books. In particular, I would like to mention the construction of two-level resolution IV designs in Chapter 11." -Zentralblatt MATH 1306

Preface xv
1 Introduction
1(14)
2 Linear Model Basics
15(16)
2.1 Least squares
15(2)
2.2 Estimation of σ2
17(1)
2.3 F-test
18(1)
2.4 One-way layout
19(1)
2.5 Estimation of a subset of parameters
20(2)
2.6 Hypothesis testing for a subset of parameters
22(1)
2.7 Adjusted orthogonality
23(1)
2.8 Additive two-way layout
24(3)
2.9 The case of proportional frequencies
27(4)
3 Randomization and Blocking
31(8)
3.1 Randomization
31(1)
3.2 Assumption of additivity and models for completely randomized designs
32(1)
3.3 Randomized block designs
33(1)
3.4 Randomized row-column designs
34(1)
3.5 Nested row-column designs and blocked split-plot designs
35(1)
3.6 Randomization model*
36(3)
4 Factors
39(12)
4.1 Factors as partitions
39(1)
4.2 Block structures and Hasse diagrams
40(2)
4.3 Some matrices and spaces associated with factors
42(2)
4.4 Orthogonal projections, averages, and sums of squares
44(1)
4.5 Condition of proportional frequencies
45(1)
4.6 Supremums and infimums of factors
46(1)
4.7 Orthogonality of factors
47(4)
5 Analysis of Some Simple Orthogonal Designs
51(20)
5.1 A general result
51(4)
5.2 Completely randomized designs
55(2)
5.3 Null ANOVA for block designs
57(2)
5.4 Randomized complete block designs
59(1)
5.5 Randomized Latin square designs
60(2)
5.6 Decomposition of the treatment sum of squares
62(1)
5.7 Orthogonal polynomials
63(2)
5.8 Orthogonal and nonorthogonal designs
65(2)
5.9 Models with fixed block effects
67(4)
6 Factorial Treatment Structure and Complete Factorial Designs
71(22)
6.1 Factorial effects for two and three two-level factors
71(4)
6.2 Factorial effects for more than three two-level factors
75(2)
6.3 The general case
77(4)
6.4 Analysis of complete factorial designs
81(2)
6.5 Analysis of unreplicated experiments
83(1)
6.6 Defining factorial effects via finite geometries
84(3)
6.7 Defining factorial effects via Abelian groups
87(3)
6.8 More on factorial treatment structure*
90(3)
7 Blocked, Split-Plot, and Strip-Plot Complete Factorial Designs
93(24)
7.1 An example
93(2)
7.2 Construction of blocked complete factorial designs
95(3)
7.3 Analysis
98(1)
7.4 Pseudo factors
99(1)
7.5 Partial confounding
99(1)
7.6 Design keys
100(4)
7.7 A template for design keys
104(2)
7.8 Construction of blocking schemes via Abelian groups
106(2)
7.9 Complete factorial experiments in row-column designs
108(2)
7.10 Split-plot designs
110(5)
7.11 Strip-plot designs
115(2)
8 Fractional Factorial Designs and Orthogonal Arrays
117(22)
8.1 Treatment models for fractional factorial designs
117(1)
8.2 Orthogonal arrays
118(4)
8.3 Examples of orthogonal arrays
122(2)
8.4 Regular fractional factorial designs
124(1)
8.5 Designs derived from Hadamard matrices
125(3)
8.6 Mutually orthogonal Latin squares and orthogonal arrays
128(1)
8.7 Foldover designs
128(2)
8.8 Difference matrices
130(3)
8.9 Enumeration of orthogonal arrays
133(1)
8.10 Some variants of orthogonal arrays*
134(5)
9 Regular Fractional Factorial Designs
139(30)
9.1 Construction and defining relation
139(3)
9.2 Aliasing and estimability
142(3)
9.3 Analysis
145(2)
9.4 Resolution
147(1)
9.5 Regular fractional factorial designs are orthogonal arrays
147(4)
9.6 Foldovers of regular fractional factorial designs
151(4)
9.7 Construction of designs for estimating required effects
155(2)
9.8 Grouping and replacement
157(4)
9.9 Connection with linear codes
161(1)
9.10 Factor representation and labeling
162(2)
9.11 Connection with finite projective geometry*
164(2)
9.12 Foldover and even designs revisited*
166(3)
10 Minimum Aberration and Related Criteria
169(26)
10.1 Minimum aberration
169(1)
10.2 Clear two-factor interactions
170(1)
10.3 Interpreting minimum aberration
171(2)
10.4 Estimation capacity
173(5)
10.5 Other justifications of minimum aberration
178(1)
10.6 Construction and complementary design theory
179(4)
10.7 Maximum estimation capacity: a projective geometric approach*
183(2)
10.8 Clear two-factor interactions revisited
185(2)
10.9 Minimum aberration blocking of complete factorial designs
187(1)
10.10 Minimum moment aberration
188(2)
10.11 A Bayesian approach
190(5)
11 Structures and Construction of Two-Level Resolution IV Designs
195(28)
11.1 Maximal designs
195(1)
11.2 Second-order saturated designs
196(3)
11.3 Doubling
199(3)
11.4 Maximal designs with N/4 + 1 ≤n≤N/2
202(2)
11.5 Maximal designs with n = N/4 + 1
204(3)
11.6 Partial foldover
207(2)
11.7 More on clear two-factor interactions
209(2)
11.8 Applications to minimum aberration designs
211(2)
11.9 Minimum aberration even designs
213(3)
11.10 Complementary design theory for doubling
216(4)
11.11 Proofs of Theorems 11.28 and 11.29*
220(1)
11.12 Coding and projective geometric connections*
221(2)
12 Orthogonal Block Structures and Strata
223(34)
12.1 Nesting and crossing operators
223(5)
12.2 Simple block structures
228(2)
12.3 Statistical models
230(2)
12.4 Poset block structures
232(1)
12.5 Orthogonal block structures
233(1)
12.6 Models with random effects
234(2)
12.7 Strata
236(2)
12.8 Null ANOVA
238(1)
12.9 Nelder's rules
239(3)
12.10 Determining strata from Hasse diagrams
242(2)
12.11 Proofs of Theorems 12.6 and 12.7
244(1)
12.12 Models with random effects revisited
245(2)
12.13 Experiments with multiple processing stages
247(4)
12.14 Randomization justification of the models for simple block structures*
251(2)
12.15 Justification of Nelder's rules*
253(4)
13 Complete Factorial Designs with Orthogonal Block Structures
257(34)
13.1 Orthogonal designs
257(2)
13.2 Blocked complete factorial split-plot designs
259(4)
13.3 Blocked complete factorial strip-plot designs
263(2)
13.4 Contrasts in the strata of simple block structures
265(4)
13.5 Construction of designs with simple block structures
269(2)
13.6 Design keys
271(2)
13.7 Design key templates for blocked split-plot and strip-plot designs
273(5)
13.8 Proof of Theorem 13.2
278(1)
13.9 Treatment structures
279(1)
13.10 Checking design orthogonality
280(2)
13.11 Experiments with multiple processing stages: the nonoverlapping case
282(6)
13.12 Experiments with multiple processing stages: the overlapping case
288(3)
14 Multi-Stratum Fractional Factorial Designs
291(38)
14.1 A general procedure
291(1)
14.2 Construction of blocked regular fractional factorial designs
292(3)
14.3 Fractional factorial split-plot designs
295(5)
14.4 Blocked fractional factorial split-plot designs
300(2)
14.5 Fractional factorial strip-plot designs
302(3)
14.6 Design key construction of blocked strip-plot designs
305(1)
14.7 Post-fractionated strip-plot designs
306(2)
14.8 Criteria for selecting blocked fractional factorial designs based on modified wordlength patterns
308(2)
14.9 Fixed block effects: surrogate for maximum estimation capacity
310(2)
14.10 Information capacity and its surrogate
312(5)
14.11 Selection of fractional factorial split-plot designs
317(2)
14.12 A general result on multi-stratum fractional factorial designs
319(2)
14.13 Selection of blocked fractional factorial split-plot designs
321(1)
14.14 Selection of blocked fractional factorial strip-plot designs
322(1)
14.15 Geometric formulation*
323(6)
15 Nonregular Designs
329(36)
15.1 Indicator functions and J-characteristics
329(2)
15.2 Partial aliasing
331(1)
15.3 Projectivity
332(2)
15.4 Hidden projection properties of orthogonal arrays
334(4)
15.5 Generalized minimum aberration for two-level designs
338(2)
15.6 Generalized minimum aberration for multiple and mixed levels
340(1)
15.7 Connection with coding theory
341(2)
15.8 Complementary designs
343(2)
15.9 Minimum moment aberration
345(2)
15.10 Proof of Theorem 15.18*
347(1)
15.11 Even designs and foldover designs
348(1)
15.12 Parallel fiats designs
349(4)
15.13 Saturated designs for hierarchical models: an application of algebraic geometry
353(2)
15.14 Search designs
355(1)
15.15 Supersaturated designs
356(9)
Appendix
365(6)
A.1 Groups
365(1)
A.2 Finite fields
365(2)
A.3 Vector spaces
367(1)
A.4 Finite Euclidean geometry
368(1)
A.5 Finite projective geometry
368(1)
A.6 Orthogonal projections and orthogonal complements
369(1)
A.7 Expectation of a quadratic form
369(1)
A.8 Balanced incomplete block designs
370(1)
References 371(18)
Index 389
Ching-Shui Cheng is currently a Distinguished Research Fellow and Director of the Institute of Statistical Science, Academia Sinica, in Taiwan, and a retired professor from the University of California, Berkeley. He received his B.S. in mathematics from National Tsing Hua University and both his MS in mathematics and Ph.D. in mathematics from Cornell University. After receiving his Ph.D., he became an assistant professor in the Department of Statistics at the University of California, Berkeley. He was later promoted to associate professor and then professor. He retired on July 1, 2013. Dr. Chengs research interest is mainly in experimental design and related combinatorial problems. He is a fellow of the Institute of Mathematical Statistics and the American Statistical Association and an elected member of the International Statistical Institute. He was an associate editor of the Journal of Statistical Planning and Inference, Annals of Statistics, Statistica Sinica, Biometrika, and Technometrics. He also served as the chair-editor of Statistica Sinica from 1996 to 1999.
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