Geometrical Foundations of Asymptotic Inference

1. Auflage 1997
ISBN: 978-0-471-82668-2
Verlag: Wiley

Buch, Englisch, 376 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 762 g

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.

Autoren/Hrsg.

Kass, Robert E

Vos, Paul W

Inhaltsverzeichnis

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.

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.

Über Autor(innen)

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.