Autori
Critchley, Frank
Marriott, Paul
Salmon, Mark

Titolo
Preferred point geometry and statistical manifolds
Periodico
European University Institute of Badia Fiesolana (Fi). Department of Economics - Working papers
Anno: 1991 - Fascicolo: 51 - Pagina iniziale: 1 - Pagina finale: 26

A new mathematical object called a preferred point geometry is introduced in order to (a) provide a natural geometric framework in which to do statistical inference and (b) reflect the distinction between homogeneous aspects (e.g. all points 0 in 0 are treated equally) and preferred point ones (e.g. when one point, is isolated i.e. if 0q is the true parameter). Although preferred point geometry is applicable generally in statistics, we focus here on its ability to encompass and extend the theoretical structure of Statistical Manifolds developed by Lauritzen(1987),in particular to Amari's expected geometry. A symmetric conditioncharacterises when a preferred point geometry both subsum es a Statistical Manifold and simultaneously generalises it to arbitrary order; there are corresponding links to Barndorff-Nielsen's strings. The rather unnatural mixing of metric and non-metric connections in Statistical manifolds is avoid ed since all connections used are shown to be metric. An interpretation of duality of Statistical manifolds is given in terms of the relation between the score vector and the maximum likelihood estimate.




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