Critchley, Frank; Marriott, Paul and Salmon, Mark
(2002).
| DOI (Digital Object Identifier) Link: | http://doi.org/10.1016/S0378-3758(01)00115-X |
|---|---|
| Google Scholar: | Look up in Google Scholar |
Abstract
A brief synopsis of progress in differential geometry in statistics is followed by a note of some points of tension in the developing relationship between these disciplines. The preferred point nature of much of statistics is described and suggests the adoption of a corresponding geometry which reduces these tensions. Applications of preferred point geometry in statistics are then reviewed. These include extensions of statistical manifolds, a statistical interpretation of duality in Amari's expected geometry, and removal of the apparent incompatibility between (Kullback–Leibler) divergence and geodesic distance. Equivalences between a number of new expected preferred point geometries are established and a new characterisation of total flatness shown. A preferred point geometry of influence analysis is briefly indicated. Technical details are kept to a minimum throughout to improve accessibility.
| Item Type: | Journal Article |
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| ISSN: | 0378-3758 |
| Keywords: | Differential geometry; Divergence; Geodesic distance; Influence analysis; Kullback–Leibler divergence; Statistical manifold; Parametric statistical modelling; Preferred point geometry; Rao distance; Riemannian geometry; Yoke geometry |
| Academic Unit/Department: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) |
| Item ID: | 4661 |
| Depositing User: | Frank Critchley |
| Date Deposited: | 10 Jul 2006 |
| Last Modified: | 02 Aug 2016 12:58 |
| URI: | http://oro.open.ac.uk/id/eprint/4661 |
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