Preferred point [alpha]-manifold and Amari's [alpha]-connections

Hong-Tu Zhu and Bo-Cheng Wei

Statistics & Probability Letters, 1997, vol. 36, issue 3, 219-229

Abstract: We consider a new mathematical object called preferred point [alpha]-manifold, which is a natural extension of Lauritzen (1987) and Critchley et al. (1993). A sufficient and necessary condition is given to guarantee that preferred point [alpha]-geometry subsumes a statistical manifold. We obtained some properties related to Amari's expected geometry, in particular the duality in this new geometry. We also defined a new preferred point [alpha]-estimate to investigate the duality from the asymptotic statistical viewpoint. The mixture family is discussed as an illustration.

Keywords: Amari; expected; geometry; Amari's; [alpha]-connection; Mixture; family; Preferred; point; [alpha]-estimate; Preferred; point; [alpha]-geometry; Preferred; point; statistical; [alpha]-geometry (search for similar items in EconPapers)
Date: 1997
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