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Geometrical foundations of asymptotic inference. (English) Zbl 0880.62005
Wiley Series in Probability and Statistics. New York, NY: Wiley. xii, 355 p. £60.00 (1997).

This is the first book which enables us to use the notions of differential geometry in statistical inference and which provides an introduction to asymptotic statistical inference through differential geometrical methods.

The book consists of three distinct parts. Part I concerns one-dimensional curved exponential families and contains first- and second-order asymptotics. Part II sketches the multidimensional generalizations and presents additional results and methodology. Part III begins with information-metric Riemannian geometry, goes on to a version of Amari’s results using statistical manifolds together with generalizations based on divergence functions, and then briefly surveys additional recent topics such as statistical fiber bundles.

The contents are accessible to readers without previous knowledge of differential geometry.

62A01Foundations and philosophical topics in statistics
62-02Research monographs (statistics)
62-01Textbooks (statistics)