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Multivariate Statistics And Matrices In Statistics
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Book Synopsis Advanced Multivariate Statistics with Matrices by : Tõnu Kollo
Download or read book Advanced Multivariate Statistics with Matrices written by Tõnu Kollo and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents important tools and techniques for treating problems in m- ern multivariate statistics in a systematic way. The ambition is to indicate new directions as well as to present the classical part of multivariate statistical analysis in this framework. The book has been written for graduate students and statis- cians who are not afraid of matrix formalism. The goal is to provide them with a powerful toolkit for their research and to give necessary background and deeper knowledge for further studies in di?erent areas of multivariate statistics. It can also be useful for researchers in applied mathematics and for people working on data analysis and data mining who can ?nd useful methods and ideas for solving their problems. Ithasbeendesignedasatextbookforatwosemestergraduatecourseonmultiva- ate statistics. Such a course has been held at the Swedish Agricultural University in 2001/02. On the other hand, it can be used as material for series of shorter courses. In fact, Chapters 1 and 2 have been used for a graduate course ”Matrices in Statistics” at University of Tartu for the last few years, and Chapters 2 and 3 formed the material for the graduate course ”Multivariate Asymptotic Statistics” in spring 2002. An advanced course ”Multivariate Linear Models” may be based on Chapter 4. A lot of literature is available on multivariate statistical analysis written for di?- ent purposes and for people with di?erent interests, background and knowledge.
Book Synopsis The Geometry of Multivariate Statistics by : Thomas D. Wickens
Download or read book The Geometry of Multivariate Statistics written by Thomas D. Wickens and published by Psychology Press. This book was released on 2014-02-25 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: A traditional approach to developing multivariate statistical theory is algebraic. Sets of observations are represented by matrices, linear combinations are formed from these matrices by multiplying them by coefficient matrices, and useful statistics are found by imposing various criteria of optimization on these combinations. Matrix algebra is the vehicle for these calculations. A second approach is computational. Since many users find that they do not need to know the mathematical basis of the techniques as long as they have a way to transform data into results, the computation can be done by a package of computer programs that somebody else has written. An approach from this perspective emphasizes how the computer packages are used, and is usually coupled with rules that allow one to extract the most important numbers from the output and interpret them. Useful as both approaches are--particularly when combined--they can overlook an important aspect of multivariate analysis. To apply it correctly, one needs a way to conceptualize the multivariate relationships that exist among variables. This book is designed to help the reader develop a way of thinking about multivariate statistics, as well as to understand in a broader and more intuitive sense what the procedures do and how their results are interpreted. Presenting important procedures of multivariate statistical theory geometrically, the author hopes that this emphasis on the geometry will give the reader a coherent picture into which all the multivariate techniques fit.
Book Synopsis Matrix-Based Introduction to Multivariate Data Analysis by : Kohei Adachi
Download or read book Matrix-Based Introduction to Multivariate Data Analysis written by Kohei Adachi and published by Springer. This book was released on 2016-10-11 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book enables readers who may not be familiar with matrices to understand a variety of multivariate analysis procedures in matrix forms. Another feature of the book is that it emphasizes what model underlies a procedure and what objective function is optimized for fitting the model to data. The author believes that the matrix-based learning of such models and objective functions is the fastest way to comprehend multivariate data analysis. The text is arranged so that readers can intuitively capture the purposes for which multivariate analysis procedures are utilized: plain explanations of the purposes with numerical examples precede mathematical descriptions in almost every chapter. This volume is appropriate for undergraduate students who already have studied introductory statistics. Graduate students and researchers who are not familiar with matrix-intensive formulations of multivariate data analysis will also find the book useful, as it is based on modern matrix formulations with a special emphasis on singular value decomposition among theorems in matrix algebra. The book begins with an explanation of fundamental matrix operations and the matrix expressions of elementary statistics, followed by the introduction of popular multivariate procedures with advancing levels of matrix algebra chapter by chapter. This organization of the book allows readers without knowledge of matrices to deepen their understanding of multivariate data analysis.
Book Synopsis Applied Multivariate Statistical Analysis (Classic Version) by : Richard A. Johnson
Download or read book Applied Multivariate Statistical Analysis (Classic Version) written by Richard A. Johnson and published by Pearson. This book was released on 2018-03-18 with total page 808 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics-series for a complete list of titles. For courses in Multivariate Statistics, Marketing Research, Intermediate Business Statistics, Statistics in Education, and graduate-level courses in Experimental Design and Statistics. Appropriate for experimental scientists in a variety of disciplines, this market-leading text offers a readable introduction to the statistical analysis of multivariate observations. Its primary goal is to impart the knowledge necessary to make proper interpretations and select appropriate techniques for analyzing multivariate data. Ideal for a junior/senior or graduate level course that explores the statistical methods for describing and analyzing multivariate data, the text assumes two or more statistics courses as a prerequisite.
Book Synopsis Multivariate Data Analysis on Matrix Manifolds by : Nickolay Trendafilov
Download or read book Multivariate Data Analysis on Matrix Manifolds written by Nickolay Trendafilov and published by Springer Nature. This book was released on 2021-09-15 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level textbook aims to give a unified presentation and solution of several commonly used techniques for multivariate data analysis (MDA). Unlike similar texts, it treats the MDA problems as optimization problems on matrix manifolds defined by the MDA model parameters, allowing them to be solved using (free) optimization software Manopt. The book includes numerous in-text examples as well as Manopt codes and software guides, which can be applied directly or used as templates for solving similar and new problems. The first two chapters provide an overview and essential background for studying MDA, giving basic information and notations. Next, it considers several sets of matrices routinely used in MDA as parameter spaces, along with their basic topological properties. A brief introduction to matrix (Riemannian) manifolds and optimization methods on them with Manopt complete the MDA prerequisite. The remaining chapters study individual MDA techniques in depth. The number of exercises complement the main text with additional information and occasionally involve open and/or challenging research questions. Suitable fields include computational statistics, data analysis, data mining and data science, as well as theoretical computer science, machine learning and optimization. It is assumed that the readers have some familiarity with MDA and some experience with matrix analysis, computing, and optimization.
Book Synopsis Matrices for Statistics by : M. J. R. Healy
Download or read book Matrices for Statistics written by M. J. R. Healy and published by Oxford University Press. This book was released on 2000 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a concise introduction to the basis of matrix theory. The text of the first edition has been re-written and revised to take account of recent developments in statistical practice. The more difficult topics have been expanded and the mathematical explanations have been simplified. A new chapter has been included, at readers' request, to cover such topics as vectorising, matrix calculus and complex numbers.
Book Synopsis Multivariate Statistics: by : Wolfgang Härdle
Download or read book Multivariate Statistics: written by Wolfgang Härdle and published by Springer Science & Business Media. This book was released on 2007-07-27 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to Applied Multivariate Analysis with R by : Brian Everitt
Download or read book An Introduction to Applied Multivariate Analysis with R written by Brian Everitt and published by Springer Science & Business Media. This book was released on 2011-04-23 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: The majority of data sets collected by researchers in all disciplines are multivariate, meaning that several measurements, observations, or recordings are taken on each of the units in the data set. These units might be human subjects, archaeological artifacts, countries, or a vast variety of other things. In a few cases, it may be sensible to isolate each variable and study it separately, but in most instances all the variables need to be examined simultaneously in order to fully grasp the structure and key features of the data. For this purpose, one or another method of multivariate analysis might be helpful, and it is with such methods that this book is largely concerned. Multivariate analysis includes methods both for describing and exploring such data and for making formal inferences about them. The aim of all the techniques is, in general sense, to display or extract the signal in the data in the presence of noise and to find out what the data show us in the midst of their apparent chaos. An Introduction to Applied Multivariate Analysis with R explores the correct application of these methods so as to extract as much information as possible from the data at hand, particularly as some type of graphical representation, via the R software. Throughout the book, the authors give many examples of R code used to apply the multivariate techniques to multivariate data.
Book Synopsis Modern Multivariate Statistical Techniques by : Alan J. Izenman
Download or read book Modern Multivariate Statistical Techniques written by Alan J. Izenman and published by Springer Science & Business Media. This book was released on 2009-03-02 with total page 757 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book on multivariate analysis to look at large data sets which describes the state of the art in analyzing such data. Material such as database management systems is included that has never appeared in statistics books before.
Book Synopsis Methods of Multivariate Analysis by : Alvin C. Rencher
Download or read book Methods of Multivariate Analysis written by Alvin C. Rencher and published by John Wiley & Sons. This book was released on 2003-04-14 with total page 739 pages. Available in PDF, EPUB and Kindle. Book excerpt: Amstat News asked three review editors to rate their top five favorite books in the September 2003 issue. Methods of Multivariate Analysis was among those chosen. When measuring several variables on a complex experimental unit, it is often necessary to analyze the variables simultaneously, rather than isolate them and consider them individually. Multivariate analysis enables researchers to explore the joint performance of such variables and to determine the effect of each variable in the presence of the others. The Second Edition of Alvin Rencher's Methods of Multivariate Analysis provides students of all statistical backgrounds with both the fundamental and more sophisticated skills necessary to master the discipline. To illustrate multivariate applications, the author provides examples and exercises based on fifty-nine real data sets from a wide variety of scientific fields. Rencher takes a "methods" approach to his subject, with an emphasis on how students and practitioners can employ multivariate analysis in real-life situations. The Second Edition contains revised and updated chapters from the critically acclaimed First Edition as well as brand-new chapters on: Cluster analysis Multidimensional scaling Correspondence analysis Biplots Each chapter contains exercises, with corresponding answers and hints in the appendix, providing students the opportunity to test and extend their understanding of the subject. Methods of Multivariate Analysis provides an authoritative reference for statistics students as well as for practicing scientists and clinicians.
Book Synopsis Matrix Analysis for Statistics by : James R. Schott
Download or read book Matrix Analysis for Statistics written by James R. Schott and published by John Wiley & Sons. This book was released on 2016-06-20 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date version of the complete, self-contained introduction to matrix analysis theory and practice Providing accessible and in-depth coverage of the most common matrix methods now used in statistical applications, Matrix Analysis for Statistics, Third Edition features an easy-to-follow theorem/proof format. Featuring smooth transitions between topical coverage, the author carefully justifies the step-by-step process of the most common matrix methods now used in statistical applications, including eigenvalues and eigenvectors; the Moore-Penrose inverse; matrix differentiation; and the distribution of quadratic forms. An ideal introduction to matrix analysis theory and practice, Matrix Analysis for Statistics, Third Edition features: • New chapter or section coverage on inequalities, oblique projections, and antieigenvalues and antieigenvectors • Additional problems and chapter-end practice exercises at the end of each chapter • Extensive examples that are familiar and easy to understand • Self-contained chapters for flexibility in topic choice • Applications of matrix methods in least squares regression and the analyses of mean vectors and covariance matrices Matrix Analysis for Statistics, Third Edition is an ideal textbook for upper-undergraduate and graduate-level courses on matrix methods, multivariate analysis, and linear models. The book is also an excellent reference for research professionals in applied statistics. James R. Schott, PhD, is Professor in the Department of Statistics at the University of Central Florida. He has published numerous journal articles in the area of multivariate analysis. Dr. Schott’s research interests include multivariate analysis, analysis of covariance and correlation matrices, and dimensionality reduction techniques.
Book Synopsis Aspects of Multivariate Statistical Theory by : Robb J. Muirhead
Download or read book Aspects of Multivariate Statistical Theory written by Robb J. Muirhead and published by John Wiley & Sons. This book was released on 2009-09-25 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. ". . . the wealth of material on statistics concerning the multivariate normal distribution is quite exceptional. As such it is a very useful source of information for the general statistician and a must for anyone wanting to penetrate deeper into the multivariate field." -Mededelingen van het Wiskundig Genootschap "This book is a comprehensive and clearly written text on multivariate analysis from a theoretical point of view." -The Statistician Aspects of Multivariate Statistical Theory presents a classical mathematical treatment of the techniques, distributions, and inferences based on multivariate normal distribution. 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 are introduced. Advances in multivariate analysis are discussed, including decision theory and robustness. The book also includes tables of percentage points of many of the standard likelihood statistics used in multivariate statistical procedures. This definitive resource provides in-depth discussion of the multivariate field and serves admirably as both a textbook and reference.
Book Synopsis Mathematical Tools for Applied Multivariate Analysis by : Paul E. Green
Download or read book Mathematical Tools for Applied Multivariate Analysis written by Paul E. Green and published by Academic Press. This book was released on 2014-05-10 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Tools for Applied Multivariate Analysis provides information pertinent to the aspects of transformational geometry, matrix algebra, and the calculus that are most relevant for the study of multivariate analysis. This book discusses the mathematical foundations of applied multivariate analysis. Organized into six chapters, this book begins with an overview of the three problems in multiple regression, principal components analysis, and multiple discriminant analysis. This text then presents a standard treatment of the mechanics of matrix algebra, including definitions and operations on matrices, vectors, and determinants. Other chapters consider the topics of eigenstructures and linear transformations that are important to the understanding of multivariate techniques. This book discusses as well the eigenstructures and quadratic forms. The final chapter deals with the geometric aspects of linear transformations. This book is a valuable resource for students.
Book Synopsis Multivariate Statistical Inference by : Narayan C. Giri
Download or read book Multivariate Statistical Inference written by Narayan C. Giri and published by Academic Press. This book was released on 2014-07-10 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Matrix Algebra written by James E. Gentle and published by Springer Science & Business Media. This book was released on 2007-07-27 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.
Book Synopsis Multivariate Statistics: Old School by : John I. Marden
Download or read book Multivariate Statistics: Old School written by John I. Marden and published by CreateSpace. This book was released on 2015-09-14 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multivariate Statistics: Old School is amathematical and methodological introduction to multivariate statistical analysis. It presents the basic mathematical grounding that graduate statistics students need for future research, andimportant multivariate techniques useful to statisticians in general. The material provides support forfurther study in big data and machine learning. Topics include The multivariate normal and Wishart distributions Linear models, including multivariate regression and analysis of variance, andboth-sides models (GMANOVA, repeated measures, growth curves) Linear algebra useful for multivariate statistics Covariance structures, including principal components, factor analysis, independence and conditional independence, and symmetry models Classification (linear and quadratic discrimination, trees, logistic regression) Clustering (K-means, model-based, hierarchical) Other techniques, including biplots, canonical correlations, and multidimensional scaling Most of the analyses in the book use the statistical computing environment R, for which there is an available package (msos)of multivariate routines and data sets. This text was developed over many years by the author, John Marden, while teaching in the Department of Statistics, University of Illinoisat Urbana-Champaign.
Book Synopsis Multivariate Statistics and Matrices in Statistics by : E. M. Tiit
Download or read book Multivariate Statistics and Matrices in Statistics written by E. M. Tiit and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-05-18 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Multivariate Statistics and Matrices in Statistics".
