Fisher Information And α-connections For A Class Of Transformational Models

In this paper we use invariant theory for representations of groups in order to get an indirect method of computing the Fisher metric and the α-connections of transformational models parameterized by symmetric spaces. Among others these models include the Von Mises-Fisher model, the Hyperboloid model, the multivariable zero mean normal model with determinant one covariant matrix and the Wishard model.122165184Amari, S., (1985) Differential-Geometrical Methods in Statistics, Lecture Notes in Statistics, 28. , Springer, BerlinAmari, S.-I., Barndorff-Nielsen, O.E., Kass, R.E., Lauritzen, S.L., Rao, C.R., (1987) Differential Geometry in Statistical Inference, Lecture Notes-monograph Series, 10. , Institute of Mathematical Statistics, HaywardBarndorff-Nielsen, O.E., Blaesild, P., Eriksen, P., (1989) Decomposition and Invariance of Measures and Statistical Transformation Models, Lecture Notes in Statistics, 58. , Springer, New YorkCarter, R., (1972) Simple Groups of Lie Type, , Wiley & Sons, New YorkEaton, M.L., (1989) Group Invariance Applications in Statistics, NFS-CBMS Regional Conf. Series in Prob. Stat., 1. , Institute of Mathematical Statistics, HaywardHelgason, S., (1978) Differential Geometry, Lie Groups and Symmetric Spaces, , Academic Press, New YorkHumphreys, J.E., (1990) Reflection Groups and Coxeter Groups, , Cambridge University Press, CambridgeKobayashi, S., Nomizu, K., (1962) Foundations of Differential Geometry, , Wiley & Sons, New YorkLeCam, L., (1986) Asymptotic Methods in Statistical Decision Theory, , Springer, BerlinDe F. Marques, M.S., San Martin, L.A.B., Quasi-invariance of product measures under lie group perturbations: Fisher information and L2-differentiability (1992) Ann. of Probability, 20, pp. 1420-1435Warner, G., (1972) Harmonic Analysis on Semi-Simple Lie Groups, 1. , Springer, New Yor