## Hiroshima Mathematical Journal

### Any statistical manifold has a contrast function---on the $C\sp 3$-functions taking the minimum at the diagonal of the product manifold

Takao Matumoto

#### Article information

Source
Hiroshima Math. J., Volume 23, Number 2 (1993), 327-332.

Dates
First available in Project Euclid: 21 March 2008

https://projecteuclid.org/euclid.hmj/1206128255

Digital Object Identifier
doi:10.32917/hmj/1206128255

Mathematical Reviews number (MathSciNet)
MR1228574

Zentralblatt MATH identifier
0796.53036

#### Citation

Matumoto, Takao. Any statistical manifold has a contrast function---on the $C\sp 3$-functions taking the minimum at the diagonal of the product manifold. Hiroshima Math. J. 23 (1993), no. 2, 327--332. doi:10.32917/hmj/1206128255. https://projecteuclid.org/euclid.hmj/1206128255

#### References

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• [2] S.-I. Amari, O. E. Barndorff-Nielsen, R. E. Kass, S. L. Lauritzen and C. R. Rao, Differential Geometry in Statistical Inferences, IMS Lecture Notes-Monograph Series, 10, Institute of Mathematical Statistics, Hayward, 1987.
• [3] S. Eguchi, Geometry of minimum contrast, Hiroshima Math. J. 22 (1992), 631-647.
• [4] S. Kobayashi and K. Nomizu, Foundation of Differential Geometry, Interscience Publishers, New York, 1963.
• [5] S. L. Lauritzen, Statistical manifolds, in Differential Geometry in Statistical Inferences, [2] above, 1987, 163-216.
• [6] H. Rund, The Differential Geometry of Finsler Spaces, Grund. Math. Wiss., Springer-Verlag, Berlin, 1959.
• [7] H. Shima, Hessian manifolds and convexity, in Manifolds and Lie Groups, Progress in Mathematics vol. 14, Birkhauser, Boston, 1981, 385-392.