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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

MSC:

62F05 Asymptotic properties of parametric tests
62F12 Asymptotic properties of parametric estimators
53B99 Local differential geometry
53B21 Methods of local Riemannian geometry