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: 2552

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.

Bilinear Regression Analysis

An Introduction

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Author: Dietrich von Rosen

Publisher: Springer

ISBN: 3319787845

Category: Mathematics

Page: 468

View: 9631

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: Theodore W. Anderson

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 675

View: 1043

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.

Nonlinear Multivariate Analysis

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Author: Albert Gifi

Publisher: John Wiley & Sons Incorporated

ISBN: 9780471926207

Category: Mathematics

Page: 579

View: 8926

Conventions and controversies in multivariate analysis; Coding of categorical data; Homogeneity analysis; Nonlinear principal components analysis; Nonlinear generalized canonical analysis; Nonlinear canonical correlation analysis; Asymmetric treatment of sets: some special cases, some future programs; Multidimensional scaling and correspondende analysis; Models as gauges for the analysis of binary data; Reflections on restrictions; Nonlinear multivariate analysis: principles and possibilities; The study of stability; The proof of the pudding.

Multivariate Observations

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Author: George A. F. Seber

Publisher: John Wiley & Sons

ISBN: 0470317310

Category: Mathematics

Page: 686

View: 5101

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.

An Introduction to Multivariate Statistical Analysis

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Author: T. W. Anderson

Publisher: Wiley-Interscience

ISBN: 9780471360919

Category: Mathematics

Page: 752

View: 9739

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.

Multivariate Statistical Inference

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Author: Narayan C. Giri

Publisher: Academic Press

ISBN: 1483263339

Category: Mathematics

Page: 336

View: 8597

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.

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: 8712

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 Statistics:

Exercises and Solutions

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Author: Wolfgang Härdle,Wolfgang Karl Härdle,Zdeněk Hlávka

Publisher: Springer Science & Business Media

ISBN: 0387707840

Category: Computers

Page: 368

View: 7841

The authors have cleverly used exercises and their solutions to explore the concepts of multivariate data analysis. Broken down into three sections, this book has been structured to allow students in economics and finance to work their way through a well formulated exploration of this core topic. The first part of this book is devoted to graphical techniques. The second deals with multivariate random variables and presents the derivation of estimators and tests for various practical situations. The final section contains a wide variety of exercises in applied multivariate data analysis.

A Course in Mathematical Statistics

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Author: George G. Roussas

Publisher: Elsevier

ISBN: 0080493149

Category: Mathematics

Page: 572

View: 7029

A Course in Mathematical Statistics, Second Edition, contains enough material for a year-long course in probability and statistics for advanced undergraduate or first-year graduate students, or it can be used independently for a one-semester (or even one-quarter) course in probability alone. It bridges the gap between high and intermediate level texts so students without a sophisticated mathematical background can assimilate a fairly broad spectrum of the theorems and results from mathematical statistics. The coverage is extensive, and consists of probability and distribution theory, and statistical inference. * Contains 25% new material * Includes the most complete coverage of sufficiency * Transformation of Random Vectors * Sufficiency / Completeness / Exponential Families * Order Statistics * Elements of Nonparametric Density Estimation * Analysis of Variance (ANOVA) * Regression Analysis * Linear Models

Mathematical Basis of Statistics

Probability and Mathematical Statistics: A Series of Monographs and Textbooks

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Author: Jean-René Barra

Publisher: Academic Press

ISBN: 1483191443

Category: Mathematics

Page: 268

View: 3285

Mathematical Basis of Statistics provides information pertinent to the methods and the mathematical basis of statistics. This book discusses the fundamental notion of statistical space. Organized into 12 chapters, this book begins with an overview of the notion of statistical space in mathematical statistics and discusses other analogies with probability theory. This text then presents the notions of sufficiency and freedom, which are fundamental and useful in statistics but do not correspond to any notion in probability theory. Other chapters consider the theory of nonsequential tests and explain the practical meaning of the mathematical tools employed in statistics. This book discusses as well distributions used most frequently in classical statistical problems based on the normal distribution and provides relationships among these distributions. The final chapter deals with certain problems of mathematical statistics that are related to various problems of functional analysis. This book is a valuable resource for graduate and postgraduate students.

Theory and Methods of Statistics

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Author: P.K. Bhattacharya,Prabir Burman

Publisher: Academic Press

ISBN: 0128041234

Category: Mathematics

Page: 544

View: 9354

Theory and Methods of Statistics covers essential topics for advanced graduate students and professional research statisticians. This comprehensive resource covers many important areas in one manageable volume, including core subjects such as probability theory, mathematical statistics, and linear models, and various special topics, including nonparametrics, curve estimation, multivariate analysis, time series, and resampling. The book presents subjects such as "maximum likelihood and sufficiency," and is written with an intuitive, heuristic approach to build reader comprehension. It also includes many probability inequalities that are not only useful in the context of this text, but also as a resource for investigating convergence of statistical procedures. Codifies foundational information in many core areas of statistics into a comprehensive and definitive resource Serves as an excellent text for select master’s and PhD programs, as well as a professional reference Integrates numerous examples to illustrate advanced concepts Includes many probability inequalities useful for investigating convergence of statistical procedures

Multivariate analysis

future directions

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Author: Calyampudi Radhakrishna Rao

Publisher: North Holland

ISBN: N.A

Category: Mathematics

Page: 478

View: 5209

Multivariate Statistics

Exercises and Solutions

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Author: Wolfgang Karl Härdle,Zdeněk Hlávka

Publisher: Springer

ISBN: 364236005X

Category: Mathematics

Page: 362

View: 1562

The authors present tools and concepts of multivariate data analysis by means of exercises and their solutions. The first part is devoted to graphical techniques. The second part deals with multivariate random variables and presents the derivation of estimators and tests for various practical situations. The last part introduces a wide variety of exercises in applied multivariate data analysis. The book demonstrates the application of simple calculus and basic multivariate methods in real life situations. It contains altogether more than 250 solved exercises which can assist a university teacher in setting up a modern multivariate analysis course. All computer-based exercises are available in the R language. All data sets are included in the library SMSdata that may be downloaded via the quantlet download center www.quantlet.org. Data sets are available also via the Springer webpage. For interactive display of low-dimensional projections of a multivariate data set, we recommend GGobi.

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: 1822

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.

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: 4835

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.

Discriminant Analysis and Statistical Pattern Recognition

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Author: Geoffrey McLachlan

Publisher: John Wiley & Sons

ISBN: 9780471691150

Category: Mathematics

Page: 526

View: 2651

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