### References

1 Efron, B. Defining the curvature of a statistical problem (with applications to second order efficiency). Ann Statist 1975, 3:1189–1217–with discussion.

2 Efron, B. The geometry of exponential families. Ann Statist 1978, 6:362–376.

3 Amari, S‐i. Differential‐Geometrical Methods in Statistics. New York:

Springer; 1990.

4 Stigler, SM. The History of Statistics.

Cambridge, MA:Belknap Press of Harvard University Press; 1986.

5 Blaesild, P. Yokes and tensors derived from yokes. Ann Inst Statist Math 1991, 43:95–113.

6 Bregman, LM. The relaxation method of finding the common points of convex sets and its application to the solution of problems in convex programming. USSR Comput Math Math Phys 1967, 7:200–217.

7 Vos, PW. A geometric approach to detecting influential cases. Ann Statist 1991, 19:1570–1581.

8 Amari, S‐i, Barndorff‐Nielsen, OE, Kass, RE, Lauritzen, SL, Rao, CR. Differential Geometry in Statistical Inference. Vol. 10. Lecture Notes‐Monograph.

Institute of Mathematical Statistics; 1987.

9 Dodson, CTJ, ed. Proceedings of the GST Workshop: Geometrization of Statistical Theory.

ULDM Publications, Department of Mathematics, Univeristy of Lancaster, 1987.

10 Murray, MK, Rice, JW. Differential Geometry and Statistics. London:

Chapman %26 Hall; 1993.

11 Kass, RE, Vos, PW. Geometrical Foundations of Asymptotic Inference.

Wiley Interscience. John Wiley %26 Sons; 1997.

12 Amari, S‐i, Nagaoka, H. Methods of Information Geometry. Vol. 191. Translations of Mathematical Monographs.

Oxford University Press and the American Mathematical Society; 2000.

13 Marriott, P, Salmon, M. Applications of Differential Geometry to Econometrics. London:

Cambridge University Press; 2000.

14 Komaki, F. On asymptotic properties of predictive distributions. Biometrika 1996, 83:299–313.

15 Barndorff‐Nielsen, OE. Likelihood and observed geometries. Ann Statist 1986, 14:856–873.

16 Vos, PW. Quasi‐likelihood or extended quasi‐likelihood? an information geometric approach. Ann Inst Statist Math 1995, 47:49–64.

17 Csiszar, I. Information type measures of difference of probability distributions and indirect observations. Studia Sci Math Hungar 1967, 2:299–318.

18 Critchley, F, Marriott, P, Salmon, M. Preferred point geometry and statistical manifolds. Ann Statist 1993, 21:1197–1224.

19 Pistone, G, Sempi, C. An infinite dimensional geometric structure on the space of all probability measures equivalent to a given one. Ann Statist 1995, 23:1543–1561.

20 Lindsay, B. Mixture models: theory, geometry, and applications. NSF‐CBMS Regional Conference Series in Probability and Statistics, 1995. ISBN 0‐940600‐32‐3. Institute of Mathematical Statistics and the American Statistical Association.

21 Cena, A, Pistone, G. Exponential statistical manifold. Ann Inst Stat Math 2007, 59:27–56.

22 Anaya‐Izquierdo, K, Critchley, F, Marriott, P, Vos, PW. Towards information geometry on the space of all distributions. Ann Inst Statist Math 2010. Submitted.

23 Marriott, P. On the local geometry of mixture models. Biometrika 2002, 89:77–89.

24 Anaya‐Izquierdo, K, Marriott, P. Local mixtures of the exponential distribution. Bernoulli 2007, 13:623–640.

25 Marriott, P. On the geometry of measurement error models. Biometrika 2003, 90:567–576.

26 Critchley, F, Marriott, P. Data‐informed influence analysis. Biometrika 2004, 91:125–140.

27 McCullagh, P. Tensor Methods.

London: Chapman %26 Hall; 1987.

28 Marriott, P, Vos, PW. On the global geometry of parametric models and information recovery. Bernoulli 2004, 10:639–649.