Geometrical Foundations of Asymptotic Inference

Robert E. Kass, Paul W. Vos

ISBN 10: 0471826685 / ISBN 13: 9780471826682

Published by John Wiley and Sons Inc, US, 1997

About this Item

Die asymptotische Interferenz ist ein wichtiges statistisches Problem. Eine geometrische Formulierung ausgehend von einem einfache, präzisen und konzeptuellen Ansatz stellen die Autoren dieses Buches vor.

Seller Inventory # LU-9780471826682

Bibliographic Details

• Title: Geometrical Foundations of Asymptotic Inference
• Publisher: John Wiley and Sons Inc, US
• Publication Date: 1997
• Language: English
• ISBN 10: 0471826685
• ISBN 13: 9780471826682
• Binding: Hardback
• Condition: New
• Weight: 739 grams

About this title

Synopsis

Differential geometry provides an aesthetically appealing and oftenrevealing view of statistical inference. Beginning with anelementary treatment of one-parameter statistical models and endingwith an overview of recent developments, this is the first book toprovide an introduction to the subject that is largely accessibleto readers not already familiar with differential geometry. It alsogives a streamlined entry into the field to readers with richermathematical backgrounds. Much space is devoted to curvedexponential families, which are of interest not only because theymay be studied geometrically but also because they are analyticallyconvenient, so that results may be derived rigorously. In addition,several appendices provide useful mathematical material on basicconcepts in differential geometry. Topics covered include thefollowing:
* Basic properties of curved exponential families
* Elements of second-order, asymptotic theory
* The Fisher-Efron-Amari theory of information loss and recovery
* Jeffreys-Rao information-metric Riemannian geometry
* Curvature measures of nonlinearity
* Geometrically motivated diagnostics for exponential familyregression
* Geometrical theory of divergence functions
* A classification of and introduction to additional work in thefield

About the Author

ROBERT E. KASS is Professor and Head of the Department of Statistics at Carnegie Mellon University. PAUL W. VOS is Associate Professor of Biostatistics at East Carolina University. Both authors received their PhDs from the University of Chicago.