Geometrical Foundations of Asymptotic Inference: 125 (Wiley Series in Probability and Statistics) - Hardcover

Kass, Robert E.; Vos, Paul W.

 
9780471826682: Geometrical Foundations of Asymptotic Inference: 125 (Wiley Series in Probability and Statistics)
Hardcover
ISBN 10: 0471826685 ISBN 13: 9780471826682
Publisher: Wiley-Interscience, 1997

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

"synopsis" may belong to another edition of this title.

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.

From the Back Cover

Differential geometry provides an aesthetically appealing and often revealing view of statistical inference. Beginning with an elementary treatment of one-parameter statistical models and ending with an overview of recent developments, this is the first book to provide an introduction to the subject that is largely accessible to readers not already familiar with differential geometry. It also gives a streamlined entry into the field to readers with richer mathematical backgrounds. Much space is devoted to curved exponential families, which are of interest not only because they may be studied geometrically but also because they are analytically convenient, so that results may be derived rigorously. In addition, several appendices provide useful mathematical material on basic concepts in differential geometry. Topics covered include the following:

  • 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 family regression
  • Geometrical theory of divergence functions
  • A classification of and introduction to additional work in the field

From the Inside Flap

Differential geometry provides an aesthetically appealing and often revealing view of statistical inference. Beginning with an elementary treatment of one-parameter statistical models and ending with an overview of recent developments, this is the first book to provide an introduction to the subject that is largely accessible to readers not already familiar with differential geometry. It also gives a streamlined entry into the field to readers with richer mathematical backgrounds. Much space is devoted to curved exponential families, which are of interest not only because they may be studied geometrically but also because they are analytically convenient, so that results may be derived rigorously. In addition, several appendices provide useful mathematical material on basic concepts in differential geometry. Topics covered include the following:

  • 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 family regression
  • Geometrical theory of divergence functions
  • A classification of and introduction to additional work in the field

"About this title" may belong to another edition of this title.

Publisher
Wiley-Interscience
Publication date
1997
Language
English
ISBN 10 
0471826685
ISBN 13 
9780471826682
Binding
Hardcover
Edition number
1
Number of pages
384