Procrustes Problems
Series: Oxford Statistical Science Series; 30;
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Product details:
- Publisher OUP Oxford
- Date of Publication 22 January 2004
- ISBN 9780198510581
- Binding Hardback
- No. of pages248 pages
- Size 242x161x17 mm
- Weight 471 g
- Language English 0
Categories
Short description:
Procrustean methods are used to transform one set of data to represent another set of data as closely as possible. The name derives from the Greek myth where Procrustes invited passers-by in for a pleasant meal and a night's rest on a magical bed that would exactly fit any guest. He then either stretched the guest on the rack or cut off their legs to make them fit perfectly into the bed. Theseus turned the tables on Procrustes, fatally adjusting him to fit his own bed. The text is the first systematic overview of Procrustean methods in one volume, presenting a unifying Analysis of Variance framework for different matching methods and the development of statistical tests.
MoreLong description:
Procrustean methods are used to transform one set of data to represent another set of data as closely as possible. The name derives from the Greek myth where Procrustes invited passers-by in for a pleasant meal and a night's rest on a magical bed that would exactly fit any guest. He then either stretched the guest on the rack or cut off their legs to make them fit perfectly into the bed. Theseus turned the tables on Procrustes, fatally adjusting him to fit his own bed.
This text, the first monograph on Procrustes methods, unifies several strands in the literature and contains much new material. It focuses on matching two or more configurations by using orthogonal, projection and oblique axes transformations. Group-average summaries play an important part and links with other group-average methods are discussed.
This is the latest in the well-established and authoritative Oxford Statistical Science Series, which includes texts and monographs covering many topics of current research interest in pure and applied statistics. Each title has an original slant even if the material included is not specifically original. The authors are leading researchers and the topics covered will be of interest to all professional statisticians, whether they be in industry, government department or research institute. Other books in the series include 23. W.J.Krzanowski: Principles of multivariate analysis: a user's perspective updated edition 24. J.Durbin and S.J.Koopman: Time series analysis by State Space Models 25. Peter J. Diggle, Patrick Heagerty, Kung-Yee Liang, Scott L. Zeger: Analysis of Longitudinal Data 2/e 26. J.K. Lindsey: Nonlinear Models in Medical Statistics 27. Peter J. Green, Nils L. Hjort & Sylvia Richardson: Highly Structured Stochastic Systems 28. Margaret S. Pepe: The Statistical Evaluation of Medical Tests for Classification and Prediction 29. Christopher G. Small and Jinfang Wang: Numerical Methods for Nonlinear Estimating Equations
This is the first comprehensive text on the topic, and will undoubtedly prove invaluable to many researchers.
Table of Contents:
Preface
Contents
Introduction
Initial transformations
Two-set Procrustes problems: generalities
Orthogonal Procrustes problems
Projection Procrustes problems
Oblique Procrustes problems
Other two-sets Procrustes problems
Weighting, scaling and missing values
Generalised Procrustes problems
Analysis of variance framework
Incorporating information on variables
Accuracy and stability
Links with other methods
Some application areas, future and conclusion
Configurations
Rotations and reflections
Orthogonal projections
Oblique axes
A minimisation problem
Symmetric matrix products
References
