α-SCALAR CURVATURE OF THE t-MANIFOLD Cho, Bong-Sik; Jung, Sun-Young;
The Fisher information matrix plays a significant role in statistical inference in connection with estimation and properties of variance of estimators. In this paper, we define the parameter space of the t-manifold using its Fisher`s matrix and characterize the t-manifold from the viewpoint of information geometry. The -scalar curvatures to the t-manifold are calculated.
Adbel-All, N. H., Abd-Ellah, H. N. and Moustafa, H. M. (2003). Information geometry and statistical manifold. Chaos, Solitons and Fractals, 15, 161-172.
Amari, S. (1982). Differential geometry of curved exponential families-curvatures and information loss. Ann. Statist. 10.
Amari, S. (1985). Differential geometrical methods in statistics, Springer Lecture Notes in Statistics, 28.
Arwini, K. A. and Dodson, C. T. J. (2007). Alpha-geometry of the Weibull manifold. Second Basic Sciences Conference, Al-Fatah University, Tripoli, Libya 4-8.
Cho, B. S. and Baek, H. Y. (2006). Geometric properties of t-distribution. Honam Mathematical Journal. 28, 433-438.
Efron, B. (1975). Defining the curvature of a statistical problem. Annual. Statis- tics. 3, 1109-1242.
Kass, R. E. and Vos, P. W. (1997). Geometrical foundations of asymptotic infer ence, John Wiley and Sons, Inc.
Kass, R. E. (1989). The geometry of asymptotic inference, Statistical Science, 4, 188-219.
Murray, M. K. and Rice, J. W. (1993). Differential geometry and Statistics, Chapman and Hall, New York.
Rao, C. R. (1945). Information and the accuracy attainable in estimation of statistical parameters, Bull. Calcutta Math. Soc, 37, 81-91.