Multivariate analysis

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Author: K. V. Mardia,John T. Kent,John M. Bibby

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 521

View: 907

Multivariate Analysis deals with observations on more than one variable where there is some inherent interdependence between the variables. With several texts already available in this area, one may very well enquire of the authors as to the need for yet another book. Most of the available books fall into two categories, either theoretical or data analytic. The present book not only combines the two approaches but it also has been guided by the need to give suitable matter for the beginner as well as illustrating some deeper aspects of the subject for the research worker. Practical examples are kept to the forefront and, wherever feasible, each technique is motivated by such an example.

Multivariate Statistical Inference

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Author: Narayan C. Giri

Publisher: Academic Press

ISBN: 1483263339

Category: Mathematics

Page: 336

View: 1605

Multivariate Statistical Inference is a 10-chapter text that covers the theoretical and applied aspects of multivariate analysis, specifically the multivariate normal distribution using the invariance approach. Chapter I contains some special results regarding characteristic roots and vectors, and partitioned submatrices of real and complex matrices, as well as some special theorems on real and complex matrices useful in multivariate analysis. Chapter II deals with the theory of groups and related results that are useful for the development of invariant statistical test procedures, including the Jacobians of some specific transformations that are useful for deriving multivariate sampling distributions. Chapter III is devoted to basic notions of multivariate distributions and the principle of invariance in statistical testing of hypotheses. Chapters IV and V deal with the study of the real multivariate normal distribution through the probability density function and through a simple characterization and the maximum likelihood estimators of the parameters of the multivariate normal distribution and their optimum properties. Chapter VI tackles a systematic derivation of basic multivariate sampling distributions for the real case, while Chapter VII explores the tests and confidence regions of mean vectors of multivariate normal populations with known and unknown covariance matrices and their optimum properties. Chapter VIII is devoted to a systematic derivation of tests concerning covariance matrices and mean vectors of multivariate normal populations and to the study of their optimum properties. Chapters IX and X look into a treatment of discriminant analysis and the different covariance models and their analysis for the multivariate normal distribution. These chapters also deal with the principal components, factor models, canonical correlations, and time series. This book will prove useful to statisticians, mathematicians, and advance mathematics students.

Bilinear Regression Analysis

An Introduction

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Author: Dietrich von Rosen

Publisher: Springer

ISBN: 3319787845

Category: Mathematics

Page: 468

View: 4427

This book expands on the classical statistical multivariate analysis theory by focusing on bilinear regression models, a class of models comprising the classical growth curve model and its extensions. In order to analyze the bilinear regression models in an interpretable way, concepts from linear models are extended and applied to tensor spaces. Further, the book considers decompositions of tensor products into natural subspaces, and addresses maximum likelihood estimation, residual analysis, influential observation analysis and testing hypotheses, where properties of estimators such as moments, asymptotic distributions or approximations of distributions are also studied. Throughout the text, examples and several analyzed data sets illustrate the different approaches, and fresh insights into classical multivariate analysis are provided. This monograph is of interest to researchers and Ph.D. students in mathematical statistics, signal processing and other fields where statistical multivariate analysis is utilized. It can also be used as a text for second graduate-level courses on multivariate analysis.

An Introduction to Multivariate Statistical Analysis

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Author: T. W. Anderson

Publisher: Wiley-Interscience

ISBN: 9780471360919

Category: Mathematics

Page: 752

View: 7114

Perfected over three editions and more than forty years, this field- and classroom-tested reference: * Uses the method of maximum likelihood to a large extent to ensure reasonable, and in some cases optimal procedures. * Treats all the basic and important topics in multivariate statistics. * Adds two new chapters, along with a number of new sections. * Provides the most methodical, up-to-date information on MV statistics available.

An Introduction to Multivariate Statistical Analysis

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Author: Theodore W. Anderson

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 675

View: 1992

Multivariate Statistical Simulation Mark E. Johnson For the researcher in statistics, probability, and operations research involved in the design and execution of a computer-aided simulation study utilizing continuous multivariate distributions, this book considers the properties of such distributions from a unique perspective. With enhancing graphics (three-dimensional and contour plots), it presents generation algorithms revealing features of the distribution undisclosed in preliminary algebraic manipulations. Well-known multivariate distributions covered include normal mixtures, elliptically assymmetric, Johnson translation, Khintine, and Burr-Pareto-logistic. 1987 (0 471-82290-6) 230 pp. Aspects of Multivariate Statistical Theory Robb J. Muirhead A classical mathematical treatment of the techniques, distributions, and inferences based on the multivariate normal distributions. The main focus is on distribution theory—both exact and asymptotic. Introduces three main areas of current activity overlooked or inadequately covered in existing texts: noncentral distribution theory, decision theoretic estimation of the parameters of a multivariate normal distribution, and the uses of spherical and elliptical distributions in multivariate analysis. 1982 (0 471-09442-0) 673 pp. Multivariate Observations G. A. F. Seber This up-to-date, comprehensive sourcebook treats data-oriented techniques and classical methods. It concerns the external analysis of differences among objects, and the internal analysis of how the variables measured relate to one another within objects. The scope ranges from the practical problems of graphically representing high dimensional data to the theoretical problems relating to matrices of random variables. 1984 (0 471-88104-X) 686 pp.

Methods for Statistical Data Analysis of Multivariate Observations

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Author: R. Gnanadesikan

Publisher: John Wiley & Sons

ISBN: 1118030923

Category: Mathematics

Page: 384

View: 4844

A practical guide for multivariate statistical techniques-- nowupdated and revised In recent years, innovations in computer technology and statisticalmethodologies have dramatically altered the landscape ofmultivariate data analysis. This new edition of Methods forStatistical Data Analysis of Multivariate Observations explorescurrent multivariate concepts and techniques while retaining thesame practical focus of its predecessor. It integrates methods anddata-based interpretations relevant to multivariate analysis in away that addresses real-world problems arising in many areas ofinterest. Greatly revised and updated, this Second Edition provides helpfulexamples, graphical orientation, numerous illustrations, and anappendix detailing statistical software, including the S (or Splus)and SAS systems. It also offers * An expanded chapter on cluster analysis that covers advances inpattern recognition * New sections on inputs to clustering algorithms and aids forinterpreting the results of cluster analysis * An exploration of some new techniques of summarization andexposure * New graphical methods for assessing the separations among theeigenvalues of a correlation matrix and for comparing sets ofeigenvectors * Knowledge gained from advances in robust estimation anddistributional models that are slightly broader than themultivariate normal This Second Edition is invaluable for graduate students, appliedstatisticians, engineers, and scientists wishing to usemultivariate techniques in a variety of disciplines.

Multivariate Statistical Simulation

A Guide to Selecting and Generating Continuous Multivariate Distributions

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Author: Mark E. Johnson,Johnson Mark E

Publisher: John Wiley & Sons

ISBN: 9780471822905

Category: Mathematics

Page: 230

View: 9941

Provides state-of-the-art coverage for the researcher confronted with designing and executing a simulation study using continuous multivariate distributions. Concise writing style makes the book accessible to a wide audience. Well-known multivariate distributions are described, emphasizing a few representative cases from each distribution. Coverage includes Pearson Types II and VII elliptically contoured distributions, Khintchine distributions, and the unifying class for the Burr, Pareto, and logistic distributions. Extensively illustrated--the figures are unique, attractive, and reveal very nicely what distributions ``look like.'' Contains an extensive and up-to-date bibliography culled from journals in statistics, operations research, mathematics, and computer science.

Multivariate Observations

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Author: George A. F. Seber

Publisher: John Wiley & Sons

ISBN: 0470317310

Category: Mathematics

Page: 686

View: 1731

WILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. "In recent years many monographs have been published on specialized aspects of multivariate data-analysis–on cluster analysis, multidimensional scaling, correspondence analysis, developments of discriminant analysis, graphical methods, classification, and so on. This book is an attempt to review these newer methods together with the classical theory. . . . This one merits two cheers." –J. C. Gower, Department of Statistics Rothamsted Experimental Station, Harpenden, U.K. Review in Biometrics, June 1987 Multivariate Observations is a comprehensive sourcebook that treats data-oriented techniques as well as classical methods. Emphasis is on principles rather than mathematical detail, and coverage ranges from the practical problems of graphically representing high-dimensional data to the theoretical problems relating to matrices of random variables. Each chapter serves as a self-contained survey of a specific topic. The book includes many numerical examples and over 1,100 references.

Graphical models in applied multivariate statistics

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Author: Joe Whittaker

Publisher: John Wiley & Sons Inc

ISBN: N.A

Category: Business & Economics

Page: 448

View: 8943

Graphical models--a subset of log-linear models--reveal the interrelationships between multiple variables and features of the underlying conditional independence. Following the theorem-proof-remarks format, this introduction to the use of graphical models in the description and modeling of multivariate systems covers conditional independence, several types of independence graphs, Gaussian models, issues in model selection, regression and decomposition. Many numerical examples and exercises with solutions are included.

Multivariate statistics

a vector space approach

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Author: Morris L. Eaton

Publisher: Inst of Mathematical Statistic

ISBN: 9780940600690

Category: Mathematics

Page: 512

View: 4059

Building from his lecture notes, Eaton (mathematics, U. of Minnesota) has designed this text to support either a one-year class in graduate-level multivariate courses or independent study. He presents a version of multivariate statistical theory in which vector space and invariance methods replace to a large extent more traditional multivariate methods. Using extensive examples and exercises Eaton describes vector space theory, random vectors, the normal distribution on a vector space, linear statistical models, matrix factorization and Jacobians, topological groups and invariant measures, first applications of invariance, the Wishart distribution, inferences for means in multivariate linear models and canonical correlation coefficients. Eaton also provides comments on selected exercises and a bibliography.

Principles of Multivariate Analysis

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Author: W. J. Krzanowski

Publisher: Oxford University Press

ISBN: 0198507089

Category: Mathematics

Page: 586

View: 3767

"Overall this volume provides an up-to-date and readable account of the subject, both for students of statistics and for research workers in subjects as diverse as anthropology, education, industry, medicine, and taxonomy."--BOOK JACKET.

Nonlinear statistical models

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Author: A. Ronald Gallant

Publisher: John Wiley & Sons

ISBN: 9780471802600

Category: Business & Economics

Page: 610

View: 3883

A comprehensive text and reference bringing together advances in the theory of probability and statistics and relating them to applications. The three major categories of statistical models that relate dependent variables to explanatory variables are covered: univariate regression models, multivariate regression models, and simultaneous equations models. Methods are illustrated with worked examples, complete with figures that display code and output.

Probability inequalities in multivariate distributions

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Author: Yung Liang Tong

Publisher: Academic Pr

ISBN: N.A

Category: Mathematics

Page: 239

View: 1836

Inequalities for multivariate normal distribution; Inequalities for other well-known distributions; Integral inequalities over a symmetric convex set; Inequalities via dependence association and mixture; Inequalities via majorization and weak majorization; Distribution-free inequalities; Some applications.

Discriminant Analysis and Statistical Pattern Recognition

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Author: Geoffrey McLachlan

Publisher: John Wiley & Sons

ISBN: 9780471691150

Category: Mathematics

Page: 526

View: 3569

The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. "Survey Errors and Survey Costs is a well-written, well-presented, and highly readable text that should be on every error-conscious statistician?s bookshelf. Any courses that cover the theory and design of surveys should certainly have Survey Errors and Survey Costs on their reading lists." ?Phil Edwards MEL, Aston University Science Park, UK Review in The Statistician, Vol. 40, No. 3, 1991 "This volume is an extremely valuable contribution to survey methodology. It has many virtues: First, it provides a framework in which survey errors can be segregated by sources. Second, Groves has skillfully synthesized existing knowledge, bringing together in an easily accessible form empirical knowledge from a variety of sources. Third, he has managed to integrate into a common framework the contributions of several disciplines. For example, the work of psychometricians and cognitive psychologists is made relevant to the research of econometricians as well as the field experience of sociologists. Finally, but not least, Groves has managed to present all this in a style that is accessible to a wide variety of readers ranging from survey specialists to policymakers." ?Peter H. Rossi University of Massachusetts at Amherst Review in Journal of Official Statistics, January 1991