A Calculus for Factorial Arrangements / by Sudhir Gupta, Rahul Mukerjee.
Factorial designs were introduced and popularized by Fisher (1935). Among the early authors, Yates (1937) considered both symmetric and asymmetric factorial designs. Bose and Kishen (1940) and Bose (1947) developed a mathematical theory for symmetric priIi't & -powered factorials while Nair...
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| Format: | eBook |
| Language: | English |
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New York, NY :
Springer New York : Imprint : Springer,
1989.
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| Series: | Lecture notes in statistics (Springer-Verlag) ;
59. |
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Table of Contents:
- 1. Introduction
- 2. A Calculus For Factorial Arrangements
- Elements and operations of the calculus
- Orthogonal factorial structure and balance
- 3. Characterizations For Balance With Orthogonal Factorial Structure
- Algebraic characterizations
- A combinatorial characterization
- A review of construction procedures
- Concluding remarks
- 4. Characterizations For Orthogonal Factorial Structure
- and preliminaries
- Algebraic characterizations: the connected case
- Algebraic characterizations: the disconnected case
- Partial orthogonal factorial structure
- Efficiency consistency
- 5. Constructions I: Factorial Experiments In Cyclic And Generalized Cyclic Designs
- Factorial experiments in cyclic designs
- Generalized cyclic designs
- Single replicate factorials in GC/n designs
- Further results
- Row-column designs
- Designs with partial orthogonal factorial structure
- 6. Constructions II: Designs Based On Kronecker Type Products
- Designs through ordinary Kronecker product
- Componentwise Kronecker product of order q
- Khatri-Rao product of order q
- Non-equireplicate designs
- Designs for multiway heterogeneity elimination
- 7. More On Single Replicate Factorial Designs
- General classical designs
- Bilinear classical designs
- Concluding remarks
- 8. Further Developments
- Deletion designs
- Merging of treatments
- Results on efficiency and admissibility
- Concluding remarks
- 113
- 124.