A Calculus for Factorial Arrangements. Lecture Notes in Statistics 59

Gupta, Sudhir, & Rahul Mukerjee

ISBN 10: 0387971726 / ISBN 13: 9780387971728

Editore: Springer, 1989

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Codice articolo ZB1084029

Dati bibliografici

• Titolo: A Calculus for Factorial Arrangements. Lecture Notes in Statistics 59
• Editore: Springer
• Data di pubblicazione: 1989
• Lingua: Inglese
• ISBN 10: 0387971726
• ISBN 13: 9780387971728
• Rilegatura: Brossura
• Condizione: Fine

Descrizione articolo

Riassunto

Kurkjian and Zelen (1963) gave the analysis of block designs using the calculus and Zelen and Federer (1964) applied it to the analysis of designs with two-way elimination of heterogeneity.

Contenuti

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.