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Differential-Geometrical Methods in Statistics

  • Book
  • © 1985

Overview

Authors:
  1. Shun-ichi Amari

    1. Faculty of Engineering Department of Mathematical Engineering and Information Physics, University of Tokyo, Tokyo, Japan

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Part of the book series: Lecture Notes in Statistics (LNS, volume 28)

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Table of contents (8 chapters)

  1. Front Matter

    Pages N2-V
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  2. Introduction

    1. Introduction

      • Shun-ichi Amari
      Pages 1-10

  3. Geometrical Structures of a Family of Probability Distributions

    1. Differential Geometry of Statistical Models

      • Shun-ichi Amari
      Pages 11-65

    2. α-Divergence and α-Projection in Statistical Manifold

      • Shun-ichi Amari
      Pages 66-103

  4. Higher-Order Asymptotic Theory of Statistical Inference in Curved Exponential Families

    1. Curved Exponential Families and Edgeworth Expansions

      • Shun-ichi Amari
      Pages 104-127

    2. Asymptotic Theory of Estimation

      • Shun-ichi Amari
      Pages 128-160

    3. Asymptotic Theory of Tests and Interval Estimators

      • Shun-ichi Amari
      Pages 161-209

    4. Information, Ancillarity and Conditional Inference

      • Shun-ichi Amari
      Pages 210-243

    5. Statistical Inference in the Presence of Nuisance Parameters

      • Shun-ichi Amari
      Pages 244-275

  5. Back Matter

    Pages 276-295
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Keywords

About this book

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

Authors and Affiliations

  • Faculty of Engineering Department of Mathematical Engineering and Information Physics, University of Tokyo, Tokyo, Japan

    Shun-ichi Amari

Bibliographic Information

  • Book Title: Differential-Geometrical Methods in Statistics

  • Authors: Shun-ichi Amari

  • Series Title: Lecture Notes in Statistics

  • DOI: https://doi.org/10.1007/978-1-4612-5056-2

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1985

  • Softcover ISBN: 978-0-387-96056-2Published: 14 February 1990

  • eBook ISBN: 978-1-4612-5056-2Published: 06 December 2012

  • Series ISSN: 0930-0325

  • Series E-ISSN: 2197-7186

  • Edition Number: 1

  • Number of Pages: V, 294

  • Topics: Applications of Mathematics

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