An elementary account of Amari's expected geometry

Critchley, Frank; Marriott, Paul and Salmon, Mark (2000). An elementary account of Amari's expected geometry. In: Marriott, Paul and Salmon, Mark eds. Applications of Differential Geometry to Econometrics. Cambridge, U.K.: Cambridge University Press, pp. 294–315.



Differential geometry has found fruitful application in statistical interence. 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 differential geometric approach in econometrics and statistics more generally…

The primary objective of this chapter 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 that is clearly based statistically, accessible geometrically and visually presented.

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