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

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  • Zhu, Hong-Tu
  • Wei, Bo-Cheng

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.

Suggested Citation

  • Zhu, Hong-Tu & Wei, Bo-Cheng, 1997. "Preferred point [alpha]-manifold and Amari's [alpha]-connections," Statistics & Probability Letters, Elsevier, vol. 36(3), pages 219-229, December.
    • Handle: RePEc:eee:stapro:v:36:y:1997:i:3:p:219-229
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    1. Zhu, Hong-Tu & Wei, Bo-Cheng, 1997. "Some notes on preferred point [alpha]-geometry and [alpha]-divergence function," Statistics & Probability Letters, Elsevier, vol. 33(4), pages 427-437, May.
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