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Wiley Series in Probability and Statistics Ser.: Geometrical Foundations of Asymptotic Inference by Robert E. Kass and Paul W. Vos (1997, Hardcover)
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Author Robert E. Kass, Paul W. Vos. It alsogives a streamlined entry into the field to readers with richermathematical backgrounds. Topics covered include thefollowing Basic properties of curved exponential families.
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Product Identifiers
PublisherWiley & Sons, Incorporated, John
ISBN-100471826685
ISBN-139780471826682
eBay Product ID (ePID)922013
Product Key Features
Number of Pages376 Pages
Publication NameGeometrical Foundations of Asymptotic Inference
LanguageEnglish
Publication Year1997
SubjectGeometry / Differential, Probability & Statistics / General
TypeTextbook
AuthorRobert E. Kass, Paul W. Vos
Subject AreaMathematics
SeriesWiley Series in Probability and Statistics Ser.
FormatHardcover
Dimensions
Item Height1.3 in
Item Weight26.1 Oz
Item Length9.3 in
Item Width6.3 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN96-043998
Reviews"I highly recommend this book to anyone interested in asymptotic inferences." (Statistics & Decisions, Vol.19 No. 3, 2001), "I highly recommend this book to anyone interested in asymptoticinferences." (Statistics & Decisions, Vol.19 No. 3, 2001)
Dewey Edition21
Series Volume Number125
IllustratedYes
Dewey Decimal519.54
Table Of ContentOverview 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.
SynopsisThis 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 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, 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., 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
LC Classification NumberQA276.K228 1997
