Multivariate statistics

a vector space approach

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Author: Morris L. Eaton

Publisher: John Wiley & Sons Inc

ISBN: N.A

Category: Mathematics

Page: 512

View: 1392

Multivariate Descriptive Statistical Analysis

Correspondence Analysis and Related Techniques for Large Matrices

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Author: Ludovic Lebart

Publisher: John Wiley & Sons

ISBN: N.A

Category: Analyse multivariée - Informatique

Page: 231

View: 8354

Methods of Multivariate Analysis

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Author: Alvin C. Rencher,William F. Christensen

Publisher: John Wiley & Sons

ISBN: 1118391675

Category: Mathematics

Page: 800

View: 3918

Praise for the Second Edition "This book is a systematic, well-written, well-organized text on multivariate analysis packed with intuition and insight . . . There is much practical wisdom in this book that is hard to find elsewhere." —IIE Transactions Filled with new and timely content, Methods of Multivariate Analysis, Third Edition provides examples and exercises based on more than sixty real data sets from a wide variety of scientific fields. It takes a "methods" approach to the subject, placing an emphasis on how students and practitioners can employ multivariate analysis in real-life situations. This Third Edition continues to explore the key descriptive and inferential procedures that result from multivariate analysis. Following a brief overview of the topic, the book goes on to review the fundamentals of matrix algebra, sampling from multivariate populations, and the extension of common univariate statistical procedures (including t-tests, analysis of variance, and multiple regression) to analogous multivariate techniques that involve several dependent variables. The latter half of the book describes statistical tools that are uniquely multivariate in nature, including procedures for discriminating among groups, characterizing low-dimensional latent structure in high-dimensional data, identifying clusters in data, and graphically illustrating relationships in low-dimensional space. In addition, the authors explore a wealth of newly added topics, including: Confirmatory Factor Analysis Classification Trees Dynamic Graphics Transformations to Normality Prediction for Multivariate Multiple Regression Kronecker Products and Vec Notation New exercises have been added throughout the book, allowing readers to test their comprehension of the presented material. Detailed appendices provide partial solutions as well as supplemental tables, and an accompanying FTP site features the book's data sets and related SAS® code. Requiring only a basic background in statistics, Methods of Multivariate Analysis, Third Edition is an excellent book for courses on multivariate analysis and applied statistics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for both statisticians and researchers across a wide variety of disciplines.

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: 2986

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.

Multivariate Statistics

High-Dimensional and Large-Sample Approximations

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Author: Yasunori Fujikoshi,Vladimir V. Ulyanov,Ryoichi Shimizu

Publisher: John Wiley & Sons

ISBN: 0470539860

Category: Mathematics

Page: 512

View: 3221

A comprehensive examination of high-dimensional analysis of multivariate methods and their real-world applications Multivariate Statistics: High-Dimensional and Large-Sample Approximations is the first book of its kind to explore how classical multivariate methods can be revised and used in place of conventional statistical tools. Written by prominent researchers in the field, the book focuses on high-dimensional and large-scale approximations and details the many basic multivariate methods used to achieve high levels of accuracy. The authors begin with a fundamental presentation of the basic tools and exact distributional results of multivariate statistics, and, in addition, the derivations of most distributional results are provided. Statistical methods for high-dimensional data, such as curve data, spectra, images, and DNA microarrays, are discussed. Bootstrap approximations from a methodological point of view, theoretical accuracies in MANOVA tests, and model selection criteria are also presented. Subsequent chapters feature additional topical coverage including: High-dimensional approximations of various statistics High-dimensional statistical methods Approximations with computable error bound Selection of variables based on model selection approach Statistics with error bounds and their appearance in discriminant analysis, growth curve models, generalized linear models, profile analysis, and multiple comparison Each chapter provides real-world applications and thorough analyses of the real data. In addition, approximation formulas found throughout the book are a useful tool for both practical and theoretical statisticians, and basic results on exact distributions in multivariate analysis are included in a comprehensive, yet accessible, format. Multivariate Statistics is an excellent book for courses on probability theory in statistics at the graduate level. It is also an essential reference for both practical and theoretical statisticians who are interested in multivariate analysis and who would benefit from learning the applications of analytical probabilistic methods in statistics.

The Spectral Analysis of Time Series

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Author: Lambert H. Koopmans

Publisher: Elsevier

ISBN: 9780080541563

Category: Mathematics

Page: 366

View: 3983

To tailor time series models to a particular physical problem and to follow the working of various techniques for processing and analyzing data, one must understand the basic theory of spectral (frequency domain) analysis of time series. This classic book provides an introduction to the techniques and theories of spectral analysis of time series. In a discursive style, and with minimal dependence on mathematics, the book presents the geometric structure of spectral analysis. This approach makes possible useful, intuitive interpretations of important time series parameters and provides a unified framework for an otherwise scattered collection of seemingly isolated results. The books strength lies in its applicability to the needs of readers from many disciplines with varying backgrounds in mathematics. It provides a solid foundation in spectral analysis for fields that include statistics, signal process engineering, economics, geophysics, physics, and geology. Appendices provide details and proofs for those who are advanced in math. Theories are followed by examples and applications over a wide range of topics such as meteorology, seismology, and telecommunications. Topics covered include Hilbert spaces; univariate models for spectral analysis; multivariate spectral models; sampling, aliasing, and discrete-time models; real-time filtering; digital filters; linear filters; distribution theory; sampling properties ofspectral estimates; and linear prediction. Hilbert spaces univariate models for spectral analysis multivariate spectral models sampling, aliasing, and discrete-time models real-time filtering digital filters linear filters distribution theory sampling properties of spectral estimates linear prediction

Mathematical Methods in Sample Surveys

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Author: Howard G Tucker

Publisher: World Scientific

ISBN: 981449917X

Category: Mathematics

Page: 216

View: 935

This book is about both the mathematics of sample surveys and about sample surveys. The mathematics is both elementary and rigorous. It is suitable for a one year junior-senior level course for mathematics and statistics majors as well as for students in the social sciences who are not handicapped by a fear of proofs in mathematics. It requires no previous knowledge of statistics, and it could actually serve as an introduction to statistics. A sizeable part of the book covers the discrete probability needed for the sampling methods covered. Topics then covered are: simple random sampling, sampling with unequal probabilities, linear relationships, stratified sampling, cluster sampling and two-stage sampling. Contents:Events and ProbabilityRandom VariablesExpectationConditional ExpectationLimit TheoremsSimple Random SamplingUnequal Probability SamplingLinear RelationshipsStratified SamplingCluster SamplingTwo-Stage Sampling Readership: Mathematical statisticians. keywords:Discrete Probability;Simple Random Sampling;Unequal Probability Sampling;Stratified Sampling;Cluster Sampling;Two-Stage Sampling;Ratio Estimation “The book is well written and could serve as a very good supplement to more traditional courses in mathematical statistics. It could also be recommended to interested students as a supplementary reading.” Mathematical Reviews

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: 4307

A practical guide for multivariate statistical techniques-- now updated and revised In recent years, innovations in computer technology and statistical methodologies have dramatically altered the landscape of multivariate data analysis. This new edition of Methods for Statistical Data Analysis of Multivariate Observations explores current multivariate concepts and techniques while retaining the same practical focus of its predecessor. It integrates methods and data-based interpretations relevant to multivariate analysis in a way that addresses real-world problems arising in many areas of interest. Greatly revised and updated, this Second Edition provides helpful examples, graphical orientation, numerous illustrations, and an appendix detailing statistical software, including the S (or Splus) and SAS systems. It also offers * An expanded chapter on cluster analysis that covers advances in pattern recognition * New sections on inputs to clustering algorithms and aids for interpreting the results of cluster analysis * An exploration of some new techniques of summarization and exposure * New graphical methods for assessing the separations among the eigenvalues of a correlation matrix and for comparing sets of eigenvectors * Knowledge gained from advances in robust estimation and distributional models that are slightly broader than the multivariate normal This Second Edition is invaluable for graduate students, applied statisticians, engineers, and scientists wishing to use multivariate techniques in a variety of disciplines.

Theory of Multivariate Statistics

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Author: Martin Bilodeau,David Brenner

Publisher: Springer Science & Business Media

ISBN: 0387226168

Category: Mathematics

Page: 290

View: 3032

Intended as a textbook for students taking a first graduate course in the subject, as well as for the general reference of interested research workers, this text discusses, in a readable form, developments from recently published work on certain broad topics not otherwise easily accessible, such as robust inference and the use of the bootstrap in a multivariate setting. A minimum background expected of the reader would include at least two courses in mathematical statistics, and certainly some exposure to the calculus of several variables together with the descriptive geometry of linear algebra.

Smoothing of Multivariate Data

Density Estimation and Visualization

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Author: Jussi Klemel?

Publisher: John Wiley & Sons

ISBN: 9780470425664

Category: Mathematics

Page: 640

View: 3489

An applied treatment of the key methods and state-of-the-art tools for visualizing and understanding statistical data Smoothing of Multivariate Data provides an illustrative and hands-on approach to the multivariate aspects of density estimation, emphasizing the use of visualization tools. Rather than outlining the theoretical concepts of classification and regression, this book focuses on the procedures for estimating a multivariate distribution via smoothing. The author first provides an introduction to various visualization tools that can be used to construct representations of multivariate functions, sets, data, and scales of multivariate density estimates. Next, readers are presented with an extensive review of the basic mathematical tools that are needed to asymptotically analyze the behavior of multivariate density estimators, with coverage of density classes, lower bounds, empirical processes, and manipulation of density estimates. The book concludes with an extensive toolbox of multivariate density estimators, including anisotropic kernel estimators, minimization estimators, multivariate adaptive histograms, and wavelet estimators. A completely interactive experience is encouraged, as all examples and figurescan be easily replicated using the R software package, and every chapter concludes with numerous exercises that allow readers to test their understanding of the presented techniques. The R software is freely available on the book's related Web site along with "Code" sections for each chapter that provide short instructions for working in the R environment. Combining mathematical analysis with practical implementations, Smoothing of Multivariate Data is an excellent book for courses in multivariate analysis, data analysis, and nonparametric statistics at the upper-undergraduate and graduatelevels. It also serves as a valuable reference for practitioners and researchers in the fields of statistics, computer science, economics, and engineering.

Computation of Multivariate Normal and t Probabilities

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Author: Alan Genz,Frank Bretz

Publisher: Springer Science & Business Media

ISBN: 3642016898

Category: Computers

Page: 126

View: 6900

Multivariate normal and t probabilities are needed for statistical inference in many applications. Modern statistical computation packages provide functions for the computation of these probabilities for problems with one or two variables. This book describes recently developed methods for accurate and efficient computation of the required probability values for problems with two or more variables. The book discusses methods for specialized problems as well as methods for general problems. The book includes examples that illustrate the probability computations for a variety of applications.

Bilinear Regression Analysis

An Introduction

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Author: Dietrich von Rosen

Publisher: Springer

ISBN: 3319787845

Category: Mathematics

Page: 468

View: 3928

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.

Multivariate Statistical Analysis

A Conceptual Introduction

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Author: Sam Kash Kachigan

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 303

View: 4863

This classic book provides the much needed conceptual explanations of advanced computer-based multivariate data analysis techniques: correlation and regression analysis, factor analysis, discrimination analysis, cluster analysis, multi-dimensional scaling, perceptual mapping, and more. It closes the gap between spiraling technology and its intelligent application, fulfilling the potential of both.

Introduction to Probability and Mathematical Statistics

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Author: Lee J. Bain,Max Engelhardt

Publisher: Duxbury Press

ISBN: 9780534380205

Category: Mathematics

Page: 644

View: 1211

The Second Edition of INTRODUCTION TO PROBABILITY AND MATHEMATICAL STATISTICS focuses on developing the skills to build probability (stochastic) models. Lee J. Bain and Max Engelhardt focus on the mathematical development of the subject, with examples and exercises oriented toward applications.

Multivariate Statistics

Exercises and Solutions

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Author: Wolfgang Karl Härdle,Zdeněk Hlávka

Publisher: Springer

ISBN: 364236005X

Category: Mathematics

Page: 362

View: 7262

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.

Statistical Analysis

An Interdisciplinary Introduction to Univariate & Multivariate Methods

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Author: Sam Kash Kachigan

Publisher: N.A

ISBN: N.A

Category: Business & Economics

Page: 589

View: 8640

This classic book provides the much needed conceptual explanations of advanced computer-based multivariate data analysis techniques: correlation and regression analysis, factor analysis, discrimination analysis, cluster analysis, multi-dimensional scaling, perceptual mapping, and more. It closes the gap between spiraling technology and its intelligent application, fulfilling the potential of both.

Multivariate Observations

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Author: George A. F. Seber

Publisher: John Wiley & Sons

ISBN: 0470317310

Category: Mathematics

Page: 686

View: 4263

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.