Autori
Critchley, Frank
Marriott, Paul
Salmon, Mark

Titolo
An elementary account of Amari's expected geometry
Periodico
European University Institute of Badia Fiesolana (Fi). Department of Economics - Working papers
Anno: 1994 - Fascicolo: 12 - Pagina iniziale: 1 - Pagina finale: 24

An elementary and visual account of Amari’s (1990) expected geometry is provided, focusing on the full exponential family case. Formal definitions of affine connections are not required. Rather, it is sufficient to consider the first two moments of the score function under the true distribution. Amari’s fundamental non metric affine connection appears as the natural measure of the non constancy of the true covariance of the score. This covariance is constant in the natural parameters. Non linearity of the graph of the mean score in the natural parameter is seen to reflect a curvature present in nearly all parametric families. The notion of -duality is introduced. This is a natural duality between the score function in one parametrisation and the maximum likelihood estimate in another. It is seen to correspond to, and therefore provide a statistical interpretation of, the notion of duality in Amari’s expected geometry.



Testo completo: http://hdl.handle.net/1814/492

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