Critchley, Frank; Marriott, Paul and Salmon, Mark
On preferred point geometry in statistics.
Journal of Statistical Planning and Inference, 102(2),
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.
||Differential geometry; Divergence; Geodesic distance; Influence analysis; Kullback–Leibler divergence; Statistical manifold; Parametric statistical modelling; Preferred point geometry; Rao distance; Riemannian geometry; Yoke geometry
||Mathematics, Computing and Technology > Mathematics and Statistics
||10 Jul 2006
||02 Dec 2010 19:52
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