+353-1-416-8900REST OF WORLD
+44-20-3973-8888REST OF WORLD
1-917-300-0470EAST COAST U.S
1-800-526-8630U.S. (TOLL FREE)

PRINTER FRIENDLY

Geometrical Foundations of Asymptotic Inference. Edition No. 1. Wiley Series in Probability and Statistics

  • ID: 2181438
  • Book
  • July 1997
  • 376 Pages
  • John Wiley and Sons Ltd
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
Note: Product cover images may vary from those shown
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.
Note: Product cover images may vary from those shown
Robert E. Kass Carnegie Mellon University.

Paul W. Vos School of Allied Health Sciences, East Carolina University.
Note: Product cover images may vary from those shown
Adroll
adroll