An elementary account of Amari's expected geometry
Critchley, Frank, Marriott, Paul and Salmon, Mark H. (1999) An elementary account of Amari's expected geometry. Working Paper. University of Warwick: Warwick Business School Financial Econometrics Research Centre. Working Papers Series, Vol.1999 (No.6).
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Differential geometry has found fruitful application in statistical inference.
In particular, Amari’s (1990) expected geometry is used in higher order
asymptotic analysis, and in the study of sufficiency and ancillarity. However,
we can see three drawbacks to the use of a differential geometric approach in
econometrics and statistics more generally. Firstly, the mathematics is unfamiliar
and the terms involved can be difficult for the econometrician to fully
appreciate. Secondly, their statistical meaning can be less than completely
clear, and finally the fact that, at its core, geometry is a visual subject can
be obscured by the mathematical formalism required for a rigorous analysis,
thereby hindering intuition. All three drawbacks apply particularly to the
differential geometric concept of a non metric affine connection.
The primary objective of this paper is to attempt to mitigate these drawbacks
in the case of Amari’s expected geometric structure on a full exponential
family. We aim to do this by providing an elementary account of this
structure which is clearly based statistically, accessible geometrically and
|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):||Geometry, Differential, Geometrical models in statistics|
|Series Name:||Working Papers Series|
|Publisher:||Warwick Business School Financial Econometrics Research Centre|
|Place of Publication:||University of Warwick|
|Official Date:||19 July 1999|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
|Funder:||Economic and Social Research Council (Great Britain) (ESRC)|
|Grant number:||R000232270 (ESRC)|
Amari, S. (1990), Differential-Geometrical methods in Statistics, second edition.
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