Fitting Linear Models: An Application Of Conjugate Gradient Algorithms: 10 - Brossura

Mcintosh, A.

Brossura

ISBN 10: 0387907467 ISBN 13: 9780387907468

Casa editrice: Springer, 2013

Riassunto

The increasing power and decreasing price of smalI computers, especialIy "personal" computers, has made them increasingly popular in statistical analysis. The day may not be too far off when every statistician has on his or her desktop computing power on a par with the large mainframe computers of 15 or 20 years ago.

Su questo libro

Contenuti

1. Preliminaries.- 1.1 Introduction.- 1.2 Notation Used in This Thesis.- 2. The Linear Model.- 2.1 The Gaussian Linear Model.- 2.2 Specifying an Arbitrary Model.- 2.3 Effective Balance.- 2.4 The Generalized Linear Model.- 3. The Conjugate Gradient Algorithm.- 3.1 Minimization Concepts.- 3.2 The Basic Algorithm.- 3.3 Convergence Considerations.- 3.4 The Non-Full Rank Case.- 3.5 Computational Details.- 3.6 Preconditioning.- 4. Applications: The Non-Full Rank Case.- 4.1 A Direct Sum Decomposition.- 4.2 Enumeration of Eigenvalues.- 4.3 Complete Factorial Designs.- 4.4 Other Designs.- 4.5 Preconditioning.- 5. Applications: The Full Rank Case.- 5.1 A Full Rank Parameterization.- 5.2 Hierarchical Models.- 5.3 Eigenvalues for Complete Factorial Designs.- 5.4 Other Designs.- 5.5 Preconditioning.- 6. Examples: Gaussian Linear Models.- 6.1 Implementation Details.- 6.2 The General 3-Way Case.- 6.3 A Blocked 23 Experiment.- 6.4 A Fractional 34 Experiment.- 6.5 A Quasi Latin Square Example.- 6.6 A Balanced Incomplete Block Example.- 7. Examples: Generalized Linear Models.- 7.1 Implementation Details.- 7.2 A 3x24 Loglinear Model.- 7.3 22 Loglinear Model on a Latin Square.- 7.4 A 3x22 Binomial Example.- 7.5 A Combined Loglinear and Binomial Example.- 8. Concluding Remarks.- References.- Appendices.- A. Algorithms.- A.I Hestenes-Stiefel Algorithm.- A.2 Beale Algorithm.- A.3 Preconditioned Hestenes-Stiefel Algorithm.- A.4 Hemmerle’s Algorithm with Line Search;.- A.5 Hestenes-Stiefel Algorithm with Hemmerle’s Preconditioning.- A.6 Eigenvalues, Non-Full Rank Parameterization.- A.7 Eigenvalues, Full Rank Parameterization.- B. GLIM Output.

Product Description

Book by McIntosh A

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2013
• Lingua: Inglese
• ISBN 10: 0387907467
• ISBN 13: 9780387907468
• Rilegatura: Copertina flessibile
• Numero di pagine: 208
• Contatto del produttore: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Germania