Geometrical Foundations of Asymptotic Inference 1st Edition by Robert E. Kass (PDF)

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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

User’s Reviews

Editorial Reviews: Review “I highly recommend this book to anyone interested in asymptoticinferences.” (Statistics & Decisions, Vol.19 No. 3, 2001) From the Publisher 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 differential geometry 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 and several appendices provide useful mathematical material on basic concepts in differential geometry. From the Inside Flap 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 familiesElements of second-order, asymptotic theoryThe Fisher-Efron-Amari theory of information loss and recoveryJeffreys-Rao information-metric Riemannian geometryCurvature measures of nonlinearityGeometrically motivated diagnostics for exponential family regressionGeometrical theory of divergence functionsA classification of and introduction to additional work in the field From the Back Cover 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 familiesElements of second-order, asymptotic theoryThe Fisher-Efron-Amari theory of information loss and recoveryJeffreys-Rao information-metric Riemannian geometryCurvature measures of nonlinearityGeometrically motivated diagnostics for exponential family regressionGeometrical theory of divergence functionsA classification of and introduction to additional work in the field About the Author 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. Read more

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