Robert E. Kass, Paul W. Vos

Geometrical Foundations of Asymptotic Inference (eBook, PDF)

• Format: PDF

Produktbeschreibung

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

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 376
• Erscheinungstermin: 9. September 2011
• Englisch
• ISBN-13: 9781118165973
• Artikelnr.: 38238916

Autorenporträt

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.

Inhaltsangabe

Aus dem Inhalt:
Overview and Preliminaries;
ONE-PARAMETER CURVED EXPONENTIAL FAMILIES: First-Order Asymptotics;
Second-Order Asymptotics;
MULTIPARAMETER CURVED EXPONENTIAL FAMILES: 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;
A -
Diffeomorphisms and The Inverse Function Theorem;
B -
Arclength and Curvature of Curves;
C -
Basic Concepts in Differential Geometry;
D -
A Coordinate-free Definition of Weak Sphericity.

Rezensionen

"I highly recommend this book to anyone interested in asymptoticinferences." (Statistics & Decisions, Vol.19 No. 3, 2001)