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

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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 (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:	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Status:	Not Peer Reviewed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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