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An elementary account of Amari's expected geometry

By Frank Critchley, Paul Marriott and Mark H. Salmon

Abstract

Differential geometry has found fruitful application in statistical inference.\ud In particular, Amari’s (1990) expected geometry is used in higher order\ud asymptotic analysis, and in the study of sufficiency and ancillarity. However,\ud we can see three drawbacks to the use of a differential geometric approach in\ud econometrics and statistics more generally. Firstly, the mathematics is unfamiliar\ud and the terms involved can be difficult for the econometrician to fully\ud appreciate. Secondly, their statistical meaning can be less than completely\ud clear, and finally the fact that, at its core, geometry is a visual subject can\ud be obscured by the mathematical formalism required for a rigorous analysis,\ud thereby hindering intuition. All three drawbacks apply particularly to the\ud differential geometric concept of a non metric affine connection.\ud The primary objective of this paper is to attempt to mitigate these drawbacks\ud in the case of Amari’s expected geometric structure on a full exponential\ud family. We aim to do this by providing an elementary account of this\ud structure which is clearly based statistically, accessible geometrically and\ud visually presented

Topics: QA
Publisher: Warwick Business School Financial Econometrics Research Centre
Year: 1999
OAI identifier: oai:wrap.warwick.ac.uk:1842

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