Any statistical manifold has a contrast function---on the $C\sp 3$-functions taking the minimum at the diagonal of the product manifold
Source: Hiroshima Math. J. Volume 23, Number 2 (1993), 327-332.
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Links and Identifiers
 S.-I. Amari, Differential-geometrical Methods in Statistics, Lecture Notes in Statistics 28, Springer-Verlag, Berlin, 1985.
 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.
 S. Eguchi, Geometry of minimum contrast, Hiroshima Math. J. 22 (1992), 631-647.
 S. Kobayashi and K. Nomizu, Foundation of Differential Geometry, Interscience Publishers, New York, 1963.
 S. L. Lauritzen, Statistical manifolds, in Differential Geometry in Statistical Inferences,  above, 1987, 163-216.
 H. Rund, The Differential Geometry of Finsler Spaces, Grund. Math. Wiss., Springer-Verlag, Berlin, 1959.