Critchley, Frank; Marriott, Paul and Salmon, Mark
(2002).
*Journal of Statistical Planning and Inference*, 102(2) pp. 229–245.

DOI (Digital Object Identifier) Link: | http://dx.doi.org/10.1016/S0378-3758(01)00115-X |
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## Abstract

A brief synopsis of progress in differential geometry in statistics is followed by a note of some points of tension in the developing relationship between these disciplines. The preferred point nature of much of statistics is described and suggests the adoption of a corresponding geometry which reduces these tensions. Applications of preferred point geometry in statistics are then reviewed. These include extensions of statistical manifolds, a statistical interpretation of duality in Amari's expected geometry, and removal of the apparent incompatibility between (Kullback–Leibler) divergence and geodesic distance. Equivalences between a number of new expected preferred point geometries are established and a new characterisation of total flatness shown. A preferred point geometry of influence analysis is briefly indicated. Technical details are kept to a minimum throughout to improve accessibility.

Item Type: | Journal Article |
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ISSN: | 0378-3758 |

Keywords: | Differential geometry; Divergence; Geodesic distance; Influence analysis; Kullback–Leibler divergence; Statistical manifold; Parametric statistical modelling; Preferred point geometry; Rao distance; Riemannian geometry; Yoke geometry |

Academic Unit/Department: | Mathematics, Computing and Technology > Mathematics and Statistics Mathematics, Computing and Technology |

Item ID: | 4661 |

Depositing User: | Frank Critchley |

Date Deposited: | 10 Jul 2006 |

Last Modified: | 14 Jan 2016 16:04 |

URI: | http://oro.open.ac.uk/id/eprint/4661 |

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