Author | Amari, Shun-ichi. author |
---|---|

Title | Differential-Geometrical Methods in Statistics [electronic resource] / by Shun-ichi Amari |

Imprint | New York, NY : Springer New York, 1985 |

Connect to | http://dx.doi.org/10.1007/978-1-4612-5056-2 |

Descript | V, 294 p. online resource |

SUMMARY

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

CONTENT

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

Mathematics
Applied mathematics
Engineering mathematics
Mathematics
Applications of Mathematics