论文信息 - Differential geometry of statistical inference

Differential geometry of statistical inference

A higher-order asymptotic theory of statistical inference is presented in a unified manner in the differential-geometrical framework. The first-, second- and third-order efficiencies of estimators are obtained in terms of the curvatures and connections of submanifolds related to both the model and estimator. The first-, second and third- order powers of a two-sided (unbiased) test is also obtained in terms of the curvature and the intersecting angle of the boundary of the critical region.

Shun-ichi Amari | S. Amari

[1] D. M. Chibisov. An Asymptotic Expansion for a Class of Estimators Containing Maximum Likelihood Estimators , 1974 .

[2] J. Ghosh,et al. Second order efficiency of maximum likelihood estimators , 1974 .

[3] B. Efron. Defining the Curvature of a Statistical Problem (with Applications to Second Order Efficiency) , 1975 .

[4] K. Takeuchi,et al. Asymptotic efficiency of statistical estimators : concepts and higher order asymptotic efficiency , 1981 .

[5] S. Amari. Geometrical theory of asymptotic ancillarity and conditional inference , 1982 .

[6] S. Amari. Differential Geometry of Curved Exponential Families-Curvatures and Information Loss , 1982 .

[7] J. Pfanzagl,et al. CONTRIBUTIONS TO A GENERAL ASYMPTOTIC STATISTICAL THEORY , 1982 .

[8] S. Amari,et al. Differential geometry of edgeworth expansions in curved exponential family , 1983 .

[9] S. Amari,et al. Geometrical theory of higher-order asymptotics of test, interval estimator and conditional inference , 1983, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.