Differential-Geometrical Methods in Statistics

Shun-ichi Amari (Autor)

Buch | Softcover

294 Seiten

1990
Springer-Verlag New York Inc.
978-0-387-96056-2 (ISBN)

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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

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.

Erscheint lt. Verlag	14.2.1990
Reihe/Serie	Lecture Notes in Statistics ; 28
Zusatzinfo	V, 294 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	178 x 254 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Statistik
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
ISBN-10	0-387-96056-2 / 0387960562
ISBN-13	978-0-387-96056-2 / 9780387960562
Zustand	Neuware