Differential-Geometrical Methods in Statistics

  • Shun-ichi Amari

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

Table of contents

  1. Front Matter
    Pages N2-V
  2. Introduction

    1. Shun-ichi Amari
      Pages 1-10
  3. Geometrical Structures of a Family of Probability Distributions

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

  5. Back Matter
    Pages 276-295

About this book

Introduction

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

Keywords

Estimator probability probability distribution statistical inference statistical model statistics

Authors and affiliations

  • Shun-ichi Amari
    • 1
  1. 1.Faculty of Engineering Department of Mathematical Engineering and Information PhysicsUniversity of TokyoTokyoJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-5056-2
  • Copyright Information Springer-Verlag New York 1985
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-96056-2
  • Online ISBN 978-1-4612-5056-2
  • Series Print ISSN 0930-0325
  • About this book