Amari, Shun-ichi Differential geometry of statistical inference. (English) Zbl 0533.62023 Probability theory and mathematical statistics, Proc. 4th USSR - Jap. Symp., Tbilisi/USSR 1982, Lect. Notes Math. 1021, 26-40 (1983). [For the entire collection see Zbl 0509.00020.] This is a survey paper containing without proofs the main results of the geometric theory of asymptotic statistics. This view-point, initiated by B. Efron [Ann. Stat. 3, 1189-1242 (1975; Zbl 0321.62013)], takes as starting point a submanifold of an exponential family. Then some well- known results of asymptotic inference of higher order can be formulated within a differential geometric framework considering the underlying exponential family as the basic linear object. The present paper is mainly concerned with the geometric interpretation of third order properties of estimators and tests. Reviewer: H.Strasser Cited in 3 Documents MSC: 62F05 Asymptotic properties of parametric tests 62F12 Asymptotic properties of parametric estimators 53B99 Local differential geometry 53B21 Methods of local Riemannian geometry Keywords:curvature; curved exponential families; submanifold of exponential family; survey paper; third order properties Citations:Zbl 0509.00020; Zbl 0321.62013 PDFBibTeX XML