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Geometrical Foundations Of Asymptotic Inference
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Book Synopsis Geometrical Foundations of Asymptotic Inference by : Robert E. Kass
Download or read book Geometrical Foundations of Asymptotic Inference written by Robert E. Kass and published by Wiley-Interscience. This book was released on 1997-07-17 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Geometrical Foundations of Asymptotic Inference by : Robert E. Kass
Download or read book Geometrical Foundations of Asymptotic Inference written by Robert E. Kass and published by John Wiley & Sons. This book was released on 2011-09-09 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis The Geometry of Asymptotic Inference by : Robert E. Kass
Download or read book The Geometry of Asymptotic Inference written by Robert E. Kass and published by . This book was released on 1988 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Invited Contribution to the Discussion of R.E. Kass: the Geometry of Asymptotic Inference by :
Download or read book Invited Contribution to the Discussion of R.E. Kass: the Geometry of Asymptotic Inference written by and published by . This book was released on 1989 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Invited contribution to the discussion of R.E. Kass: "The geometry of asymptotic inference" by : O. E. Barndorff-Nielsen
Download or read book Invited contribution to the discussion of R.E. Kass: "The geometry of asymptotic inference" written by O. E. Barndorff-Nielsen and published by . This book was released on 1989 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Invited Contribution to the Discussion of R.E. Kass by : Ole Eiler Barndorff-Nielsen
Download or read book Invited Contribution to the Discussion of R.E. Kass written by Ole Eiler Barndorff-Nielsen and published by . This book was released on 1989 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Research Reports written by and published by . This book was released on 1989 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential-Geometrical Methods in Statistics by : Shun-ichi Amari
Download or read book Differential-Geometrical Methods in Statistics written by Shun-ichi Amari and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "In this Lecture Note volume the author describes his differential-geometric approach to parametrical statistical problems summarizing the results he had published in a series of papers in the last five years. The author provides a geometric framework for a special class of test and estimation procedures for curved exponential families. ... ... The material and ideas presented in this volume are important and it is recommended to everybody interested in the connection between statistics and geometry ..." #Metrika#1 "More than hundred references are given showing the growing interest in differential geometry with respect to statistics. The book can only strongly be recommended to a geodesist since it offers many new insights into statistics on a familiar ground." #Manuscripta Geodaetica#2
Book Synopsis Inference and Asymptotics by : O. E. Barndorff-Nielsen
Download or read book Inference and Asymptotics written by O. E. Barndorff-Nielsen and published by Springer. This book was released on 2013-08-23 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our book Asymptotic Techniquesfor Use in Statistics was originally planned as an account of asymptotic statistical theory, but by the time we had completed the mathematical preliminaries it seemed best to publish these separately. The present book, although largely self-contained, takes up the original theme and gives a systematic account of some recent developments in asymptotic parametric inference from a likelihood-based perspective. Chapters 1-4 are relatively elementary and provide first a review of key concepts such as likelihood, sufficiency, conditionality, ancillarity, exponential families and transformation models. Then first-order asymptotic theory is set out, followed by a discussion of the need for higher-order theory. This is then developed in some generality in Chapters 5-8. A final chapter deals briefly with some more specialized issues. The discussion emphasizes concepts and techniques rather than precise mathematical verifications with full attention to regularity conditions and, especially in the less technical chapters, draws quite heavily on illustrative examples. Each chapter ends with outline further results and exercises and with bibliographic notes. Many parts of the field discussed in this book are undergoing rapid further development, and in those parts the book therefore in some respects has more the flavour of a progress report than an exposition of a largely completed theory.
Book Synopsis Asymptotic Theory Of Quantum Statistical Inference: Selected Papers by : Masahito Hayashi
Download or read book Asymptotic Theory Of Quantum Statistical Inference: Selected Papers written by Masahito Hayashi and published by World Scientific. This book was released on 2005-02-21 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum statistical inference, a research field with deep roots in the foundations of both quantum physics and mathematical statistics, has made remarkable progress since 1990. In particular, its asymptotic theory has been developed during this period. However, there has hitherto been no book covering this remarkable progress after 1990; the famous textbooks by Holevo and Helstrom deal only with research results in the earlier stage (1960s-1970s).This book presents the important and recent results of quantum statistical inference. It focuses on the asymptotic theory, which is one of the central issues of mathematical statistics and had not been investigated in quantum statistical inference until the early 1980s. It contains outstanding papers after Holevo's textbook, some of which are of great importance but are not available now.The reader is expected to have only elementary mathematical knowledge, and therefore much of the content will be accessible to graduate students as well as research workers in related fields. Introductions to quantum statistical inference have been specially written for the book. Asymptotic Theory of Quantum Statistical Inference: Selected Papers will give the reader a new insight into physics and statistical inference.
Book Synopsis A Course in Time Series Analysis by : Daniel Peña
Download or read book A Course in Time Series Analysis written by Daniel Peña and published by John Wiley & Sons. This book was released on 2011-01-25 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: New statistical methods and future directions of research in time series A Course in Time Series Analysis demonstrates how to build time series models for univariate and multivariate time series data. It brings together material previously available only in the professional literature and presents a unified view of the most advanced procedures available for time series model building. The authors begin with basic concepts in univariate time series, providing an up-to-date presentation of ARIMA models, including the Kalman filter, outlier analysis, automatic methods for building ARIMA models, and signal extraction. They then move on to advanced topics, focusing on heteroscedastic models, nonlinear time series models, Bayesian time series analysis, nonparametric time series analysis, and neural networks. Multivariate time series coverage includes presentations on vector ARMA models, cointegration, and multivariate linear systems. Special features include: Contributions from eleven of the worldâ??s leading figures in time series Shared balance between theory and application Exercise series sets Many real data examples Consistent style and clear, common notation in all contributions 60 helpful graphs and tables Requiring no previous knowledge of the subject, A Course in Time Series Analysis is an important reference and a highly useful resource for researchers and practitioners in statistics, economics, business, engineering, and environmental analysis. An Instructor's Manual presenting detailed solutions to all the problems in he book is available upon request from the Wiley editorial department.
Book Synopsis Bayesian Theory by : José M. Bernardo
Download or read book Bayesian Theory written by José M. Bernardo and published by John Wiley & Sons. This book was released on 2009-09-25 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: This highly acclaimed text, now available in paperback, provides a thorough account of key concepts and theoretical results, with particular emphasis on viewing statistical inference as a special case of decision theory. Information-theoretic concepts play a central role in the development of the theory, which provides, in particular, a detailed discussion of the problem of specification of so-called prior ignorance . The work is written from the authors s committed Bayesian perspective, but an overview of non-Bayesian theories is also provided, and each chapter contains a wide-ranging critical re-examination of controversial issues. The level of mathematics used is such that most material is accessible to readers with knowledge of advanced calculus. In particular, no knowledge of abstract measure theory is assumed, and the emphasis throughout is on statistical concepts rather than rigorous mathematics. The book will be an ideal source for all students and researchers in statistics, mathematics, decision analysis, economic and business studies, and all branches of science and engineering, who wish to further their understanding of Bayesian statistics
Book Synopsis An Introduction to Probability and Statistics by : Vijay K. Rohatgi
Download or read book An Introduction to Probability and Statistics written by Vijay K. Rohatgi and published by John Wiley & Sons. This book was released on 2011-09-15 with total page 747 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of a well-received book that was published 24 years ago and continues to sell to this day, An Introduction to Probability and Statistics is now revised to incorporate new information as well as substantial updates of existing material.
Book Synopsis Biostatistical Methods by : John M. Lachin
Download or read book Biostatistical Methods written by John M. Lachin and published by John Wiley & Sons. This book was released on 2009-09-25 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive coverage of classical and modern methods of biostatistics Biostatistical Methods focuses on the assessment of risks and relative risks on the basis of clinical investigations. It develops basic concepts and derives biostatistical methods through both the application of classical mathematical statistical tools and more modern likelihood-based theories. The first half of the book presents methods for the analysis of single and multiple 2x2 tables for cross-sectional, prospective, and retrospective (case-control) sampling, with and without matching using fixed and two-stage random effects models. The text then moves on to present a more modern likelihood- or model-based approach, which includes unconditional and conditional logistic regression; the analysis of count data and the Poisson regression model; and the analysis of event time data, including the proportional hazards and multiplicative intensity models. The book contains a technical appendix that presents the core mathematical statistical theory used for the development of classical and modern statistical methods. Biostatistical Methods: The Assessment of Relative Risks: * Presents modern biostatistical methods that are generalizations of the classical methods discussed * Emphasizes derivations, not just cookbook methods * Provides copious reference citations for further reading * Includes extensive problem sets * Employs case studies to illustrate application of methods * Illustrates all methods using the Statistical Analysis System(r) (SAS) Supplemented with numerous graphs, charts, and tables as well as a Web site for larger data sets and exercises, Biostatistical Methods: The Assessment of Relative Risks is an excellent guide for graduate-level students in biostatistics and an invaluable reference for biostatisticians, applied statisticians, and epidemiologists.
Book Synopsis Limit Distributions for Sums of Independent Random Vectors by : Mark M. Meerschaert
Download or read book Limit Distributions for Sums of Independent Random Vectors written by Mark M. Meerschaert and published by John Wiley & Sons. This book was released on 2001-07-11 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: Die Quintessenz aus über 100 Originalarbeiten! Ausgehend von den Grundpfeilern der modernen Wahrscheinlichkeitstheorie entwickeln die Autoren dieses in sich geschlossenen, gut verständlich formulierten Bandes die Theorie der unendlich teilbaren Verteilungen und der regulären Variation. Im Anschluss erarbeiten sie die allgemeine Grenzwerttheorie für unabhängige Zufallsvektoren. Dabei achten sie sorgfältig darauf, alle Aspekte in den Kontext der Wahrscheinlichkeitslehre und Statistik zu stellen und bieten dafür eine Fülle von Zusatzinformationen an.
Book Synopsis Finite Mixture Models by : Geoffrey McLachlan
Download or read book Finite Mixture Models written by Geoffrey McLachlan and published by John Wiley & Sons. This book was released on 2004-03-22 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date, comprehensive account of major issues in finitemixture modeling This volume provides an up-to-date account of the theory andapplications of modeling via finite mixture distributions. With anemphasis on the applications of mixture models in both mainstreamanalysis and other areas such as unsupervised pattern recognition,speech recognition, and medical imaging, the book describes theformulations of the finite mixture approach, details itsmethodology, discusses aspects of its implementation, andillustrates its application in many common statisticalcontexts. Major issues discussed in this book include identifiabilityproblems, actual fitting of finite mixtures through use of the EMalgorithm, properties of the maximum likelihood estimators soobtained, assessment of the number of components to be used in themixture, and the applicability of asymptotic theory in providing abasis for the solutions to some of these problems. The author alsoconsiders how the EM algorithm can be scaled to handle the fittingof mixture models to very large databases, as in data miningapplications. This comprehensive, practical guide: * Provides more than 800 references-40% published since 1995 * Includes an appendix listing available mixture software * Links statistical literature with machine learning and patternrecognition literature * Contains more than 100 helpful graphs, charts, and tables Finite Mixture Models is an important resource for both applied andtheoretical statisticians as well as for researchers in the manyareas in which finite mixture models can be used to analyze data.
Book Synopsis Nonresponse in Household Interview Surveys by : Robert M. Groves
Download or read book Nonresponse in Household Interview Surveys written by Robert M. Groves and published by John Wiley & Sons. This book was released on 2012-08-29 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive framework for both reduction of nonresponse andpostsurvey adjustment for nonresponse This book provides guidance and support for survey statisticianswho need to develop models for postsurvey adjustment fornonresponse, and for survey designers and practitioners attemptingto reduce unit nonresponse in household interview surveys. Itpresents the results of an eight-year research program that hasassembled an unprecedented data set on respondents andnonrespondents from several major household surveys in the UnitedStates. Within a comprehensive conceptual framework of influences onnonresponse, the authors investigate every aspect of surveycooperation, from the influences of household characteristics andsocial and environmental factors to the interaction betweeninterviewers and householders and the design of the surveyitself. Nonresponse in Household Interview Surveys: * Provides a theoretical framework for understanding and studyinghousehold survey nonresponse * Empirically explores the individual and combined influences ofseveral factors on nonresponse * Presents chapter introductions, summaries, and discussions onpractical implications to clarify concepts and theories * Supplies extensive references for further study and inquiry Nonresponse in Household Interview Surveys is an important resourcefor professionals and students in survey methodology/researchmethods as well as those who use survey methods or data inbusiness, government, and academia. It addresses issues critical todealing with nonresponse in surveys, reducing nonresponse duringsurvey data collection, and constructing statistical compensationsfor the effects of nonresponse on key survey estimates.
