Geometrical Foundations of Asymptotic Inference
Seiten
1997
Wiley-Interscience (Verlag)
9780471826682 (ISBN)
Wiley-Interscience (Verlag)
9780471826682 (ISBN)
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This book provides a thorough introduction to asymptotic inference. It begins with an elementary treatment of one-parameter statistical models and goes on to discuss basic properties of curved exponential families, the Fisher-Efron-Amari theory and Jeffreys-Rao Riemannian geometry based on Fisher information.
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
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
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.
Overview and Preliminaries.
ONE-PARAMETER CURVED EXPONENTIAL FAMILIES.
First-Order Asymptotics.
Second-Order Asymptotics.
MULTIPARAMETER CURVED EXPONENTIAL FAMILIES.
Extensions of Results from the One-Parameter Case.
Exponential Family Regression and Diagnostics.
Curvature in Exponential Family Regression.
DIFFERENTIAL-GEOMETRIC METHODS.
Information-Metric Riemannian Geometry.
Statistical Manifolds.
Divergence Functions.
Recent Developments.
Appendices.
References.
Indexes.
| Erscheint lt. Verlag | 25.7.1997 |
|---|---|
| Reihe/Serie | Wiley Series in Probability and Statistics |
| Sprache | englisch |
| Maße | 160 x 236 mm |
| Gewicht | 739 g |
| Themenwelt | Mathematik / Informatik ► Mathematik |
| ISBN-13 | 9780471826682 / 9780471826682 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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