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On preferred point geometry in statistics
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Critchley, Frank, Marriott, Paul and Salmon, Mark H. (2001) On preferred point geometry in statistics. Working Paper. University of Warwick: Warwick Business School Financial Econometrics Research Centre. Working Papers Series, Vol.2001 (No.4).
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Official URL: http://www2.warwick.ac.uk/fac/soc/wbs/research/wfr...
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) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Social Sciences > Warwick Business School > Financial Econometrics Research Centre Faculty of Social Sciences > Warwick Business School |
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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 | ||||
Official Date: | 2001 | ||||
Dates: |
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Volume: | Vol.2001 | ||||
Number: | No.4 | ||||
Status: | Not Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) |
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