Some notes on preferred point [alpha]-geometry and [alpha]-divergence function

Hong-Tu Zhu and Bo-Cheng Wei

Statistics & Probability Letters, 1997, vol. 33, issue 4, 427-437

Abstract: A preferred point [alpha]-geometry is introduced in this note, which is a natural extension of the work of Critchley et al. (1993, 1994). Using this geometry, the homogeneous structure and the duality are discussed. We also define a new [alpha]-divergence function and produce a flatness condition, under which the [alpha]-divergence function agrees with a squared preferred point geodesic distance. Further, the Pythagorean result given by Amari (1990) and Critchley et al. (1994) is extended to the [alpha]-divergence function.

Keywords: Amari; expected; geometry; [alpha]-divergence; function; Mixture; family; Preferred; point; [alpha]-geometry; Pythagoras'; theorem (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (1)

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