Autori
Critchley, Frank
Marriott, Paul
Salmon, Mark

Titolo
Preferred point geometry of the local differential geometry of the Kullback-Leibler divergence
Periodico
European University Institute of Badia Fiesolana (Fi). Department of Economics - Working papers
Anno: 1991 - Fascicolo: 53 - Pagina iniziale: 1 - Pagina finale: 28

The (asymmetric) Kullback-Leibler divergence function is rationalised as being geometrically a measure of preferred point geodesic distance based on path-length. This distance function is defined not on any particular parametric family but in an infinite dimensional function space in which all our finite dimensional parametric statistical families are embedded. In so doing we generalise results by Amari relating 'a-geodesic projection' to divergence functions. We are forced to consider concepts of flatness and embedding curvature. We develop a new total flatness condition under which our squared geodesic distance corresponds to twice the KullbackLeibler divegence. We show that the space of densities itself possess a form of curvature which implies in particular that only a subset of the full exponential families may in fact be considered totally flat. We study the infinite dimensional function space of finite measures in which the Kullback-Leibler divergence is most naturally viewed as a metric based measure of distance. We also propose a global measure of curvature which maybe compared with the pointwise measures of Efron and Amari.



Testo completo: http://hdl.handle.net/1814/392

Esportazione dati in Refworks (solo per utenti abilitati)