Abstract
A conformal implementation of projectively related statistical manifolds (c ∪ p—geometry) is used to introduce the notion of c ∪ p—transformations, associated to the 1-rigid action of a Lie subgroup of Conf ∩ Proj. groups.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Amari, S-i. (1985), Differential Geometrical Methods in Statistics, Lecture Notes in Statistics, 28, Springer-Verlag New York.
Rao, C.R. (1945), Bull. Calcutta Math.Soc. 37 pp 81–91
Fisher R.A. (1925), Proc. Cambridge Phil. Soc. 122 pp. 700–725
Amari, S-i.(1987) Differential Geometrical Theory of Statistics — Towards New Developments in Differential Geometry in Statistical Inference, S.S. Gupta Ed., IMS Lecture Notes-Monographs Series, 10, pp. 19–94
Chentsov, N.N. (1972) Statistical Decision and Optimal Inference, Nauka, Moscow (in Russian); translation in English, (1982) American Mathematical Society, 53, Providence, R.I.
Burdet, G., Perrin, M. Prétirage CPT 94/ P.3001.
Kobayashi, S. (1972) Transformation Groups in Differential Geometry, Springer Verlag Ed.
Gromov, M. (1988). Rigid transformation groups in Géométrie Différentielle, Travaux en cours 33, Hermann, Paris pp 65–139
Okamoto, I. Amari, S-i. Takeuchi, K. (1991) The Annals of Statistics, 19 pp. 961–981
Noguchi, M. (1992) Differential Geometry and its Applications, 2 pp. 197–222
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Burdet, G., Perrin, M. (1995). Groupes de Transformations des Varietes Statistiques. In: Bertrand, J., Flato, M., Gazeau, JP., Irac-Astaud, M., Sternheimer, D. (eds) Modern Group Theoretical Methods in Physics. Mathematical Physics Studies, vol 18. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8543-9_9
Download citation
DOI: https://doi.org/10.1007/978-94-015-8543-9_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4598-0
Online ISBN: 978-94-015-8543-9
eBook Packages: Springer Book Archive