Differential-Geometrical Methods in Statistics (Lecture Notes in Statistics 28)

**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 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 Shun-ichi Amari. Includes Index. Bibliography: P. [276]-286. 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 Front Matter....Pages N2-V Introduction....Pages 1-10 Differential Geometry of Statistical Models....Pages 11-65 α-Divergence and α-Projection in Statistical Manifold....Pages 66-103 Curved Exponential Families and Edgeworth Expansions....Pages 104-127 Asymptotic Theory of Estimation....Pages 128-160 Asymptotic Theory of Tests and Interval Estimators....Pages 161-209 Information, Ancillarity and Conditional Inference....Pages 210-243 Statistical Inference in the Presence of Nuisance Parameters....Pages 244-275 Back Matter....Pages 276-295