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On preferred point geometry in statistics
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Critchley, Frank, Marriott, Paul, 1961 and Salmon, Mark H. (Mark Howard), 1949 (2001) On preferred point geometry in statistics. Working Paper. University of Warwick: Warwick Business School Financial Econometrics Research Centre. (Working Papers Series).

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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 (KullbackLeibler) 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:  Working or Discussion Paper (Working Paper) 

Subjects:  Q Science > QA Mathematics 
Divisions:  Faculty of Social Sciences > Warwick Business School > Financial Econometrics Research Centre Faculty of Social Sciences > Warwick Business School 
Library of Congress Subject Headings (LCSH):  Geometrical models in statistics, Geometry, Differential, Distance geometry 
Series Name:  Working Papers Series 
Publisher:  Warwick Business School Financial Econometrics Research Centre 
Place of Publication:  University of Warwick 
Date:  2001 
Volume:  Vol.2001 
Number:  No.4 
Status:  Not Peer Reviewed 
Access rights to Published version:  Open Access 
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URI:  http://wrap.warwick.ac.uk/id/eprint/1823 
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