Differential-Geometrical Methods in Statistics

Softcover Nachdruck of the original 1. Auflage 1985
ISBN: 978-0-387-96056-2
Verlag: Springer

Buch, Englisch, Band 28, 294 Seiten, Format (B × H): 178 mm x 254 mm, Gewicht: 583 g

Reihe: Lecture Notes in Statistics

From the reviews: "In this Lecture Note volume the author describes his differential-geometric approach to parametrical statistical problems summarizing the results he had published in a series of papers in the last five years. The author provides a geometric framework for a special class of test and estimation procedures for curved exponential families. ... ... The material and ideas presented in this volume are important and it is recommended to everybody interested in the connection between statistics and geometry ..." #Metrika#1 "More than hundred references are given showing the growing interest in differential geometry with respect to statistics. The book can only strongly be recommended to a geodesist since it offers many new insights into statistics on a familiar ground." #Manuscripta Geodaetica#2

Zielgruppe

Research

Autoren/Hrsg.

Amari, Shun-Ichi

Inhaltsverzeichnis

1. Introduction.- I. Geometrical Structures of a Family of Probability Distributions.- 2. Differential Geometry of Statistical Models.- 3. ?-Divergence and ?-Projection in Statistical Manifold.- II. Higher-Order Asymptotic Theory of Statistical Inference in Curved Exponential Families.- 4. Curved Exponential Families and Edgeworth Expansions.- 5. Asymptotic Theory of Estimation.- 6. Asymptotic Theory of Tests and Interval Estimators.- 7. Information, Ancillarity and Conditional Inference.- 8. Statistical Inference in the Presence of Nuisance Parameters.- References.- Subject Indices.