"This textbook presents a classical approach to some techniques of multivariate analysis in a simple and transparent manner. It offers clear and concise development of the concepts; interpretation of the output of the analysis; and criteria for selection of the methods, taking into account the strengths and weaknesses of each." "This book is ideal as an advanced textbook for graduate students in statistics and other disciplines like social, biological and physical sciences. It will also be of benefit to professional statisticians." --Book Jacket.
Multivariate Statistical Methods: A Primer provides an introductory overview of multivariate methods without getting too deep into the mathematical details. This fourth edition is a revised and updated version of this bestselling introductory textbook. It retains the clear and concise style of the previous editions of the book and focuses on examples from biological and environmental sciences. The major update with this edition is that R code has been included for each of the analyses described, although in practice any standard statistical package can be used. The original idea with this book still applies. This was to make it as short as possible and enable readers to begin using multivariate methods in an intelligent manner. With updated information on multivariate analyses, new references, and R code included, this book continues to provide a timely introduction to useful tools for multivariate statistical analysis.
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.
Focusing on high-dimensional applications, this 4th edition presents the tools and concepts used in multivariate data analysis in a style that is also accessible for non-mathematicians and practitioners. All chapters include practical exercises that highlight applications in different multivariate data analysis fields. All of the examples involve high to ultra-high dimensions and represent a number of major fields in big data analysis. The fourth edition of this book on Applied Multivariate Statistical Analysis offers the following new features: A new chapter on Variable Selection (Lasso, SCAD and Elastic Net) All exercises are supplemented by R and MATLAB code that can be found on www.quantlet.de. The practical exercises include solutions that can be found in Härdle, W. and Hlavka, Z., Multivariate Statistics: Exercises and Solutions. Springer Verlag, Heidelberg.
Vector and matrix algebra; Groups and Jacobian of some transformations; Multivariate distributions and Invariance; Properties of multivariate distributions; Estimators of parameters and their functions; Basic multivariate sampling distributions; Tests of hypotheses of mean vectors; Tests concerning covariance matrices and mean vectors; Discriminant analysis; Principal components; Canonical correlations; Factor analysis.
Multivariate Statistical Analysis
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.
The death of Professor K.C. Sreedharan Pillai on June 5, 1985 was a heavy loss to many statisticians all around the world. This volume is dedicated to his memory in recog nition of his many contributions in multivariate statis tical analysis. It brings together eminent statisticians Working in multivariate analysis from around the world. The research and expository papers cover a cross-section of recent developments in the field. This volume is especially useful to researchers and to those who want to keep abreast of the latest directions in multivariate statistical analysis. I am grateful to the authors from so many different countries and research institutions who contributed to this volume. I wish to express my appreciation to all those who have reviewed the papers. The list of people include Professors T.C. Chang, So-Hsiang Chou, Dipak K. Dey, Peter Hall, Yu-Sheng Hsu, J.D. Knoke, W.J. Krzanowski, Edsel Pena, Bimal K. Sinha, Dennis L. Young, Drs. K. Krishnamoorthy, D.K. Nagar, and Messrs. Alphonse Amey, Chi-Chin Chao and Samuel Ofori-Nyarko. I wish to thank Professors Shanti S. Gupta and James 0. Berger for their keen interest and encouragement. Thanks are also due to Cynthia Patterson for her help and Reidel Publishing Com~any for their cooperation in bringing this volume out.
MULTIVARIATE STATISTICAL METHODS strikes a crucial balance between the technical information and real-world applications of multivariate statistics.
The three decades which have followed the publication of Heinz Neudecker's seminal paper `Some Theorems on Matrix Differentiation with Special Reference to Kronecker Products' in the Journal of the American Statistical Association (1969) have witnessed the growing influence of matrix analysis in many scientific disciplines. Amongst these are the disciplines to which Neudecker has contributed directly - namely econometrics, economics, psychometrics and multivariate analysis. This book aims to illustrate how powerful the tools of matrix analysis have become as weapons in the statistician's armoury. The majority of its chapters are concerned primarily with theoretical innovations, but all of them have applications in view, and some of them contain extensive illustrations of the applied techniques. This book will provide research workers and graduate students with a cross-section of innovative work in the fields of matrix methods and multivariate statistical analysis. It should be of interest to students and practitioners in a wide range of subjects which rely upon modern methods of statistical analysis. The contributors to the book are themselves practitioners of a wide range of subjects including econometrics, psychometrics, educational statistics, computation methods and electrical engineering, but they find a common ground in the methods which are represented in the book. It is envisaged that the book will serve as an important work of reference and as a source of inspiration for some years to come.
This market leader offers a readable introduction to the statistical analysis of multivariate observations. Gives readers the knowledge necessary to make proper interpretations and select appropriate techniques for analyzing multivariate data. Starts with a formulation of the population models, delineates the corresponding sample results, and liberally illustrates everything with examples. Offers an abundance of examples and exercises based on real data. Appropriate for experimental scientists in a variety of disciplines.
Multivariate statistics refer to an assortment of statistical methods that have been developed to handle situations in which multiple variables or measures are involved. Any analysis of more than two variables or measures can loosely be considered a multivariate statistical analysis. An introductory text for students learning multivariate statistical methods for the first time, this book keeps mathematical details to a minimum while conveying the basic principles. One of the principal strategies used throughout the book--in addition to the presentation of actual data analyses--is pointing out the analogy between a common univariate statistical technique and the corresponding multivariate method. Many computer examples--drawing on SAS software --are used as demonstrations. Throughout the book, the computer is used as an adjunct to the presentation of a multivariate statistical method in an empirically oriented approach. Basically, the model adopted in this book is to first present the theory of a multivariate statistical method along with the basic mathematical computations necessary for the analysis of data. Subsequently, a real world problem is discussed and an example data set is provided for analysis. Throughout the presentation and discussion of a method, many references are made to the computer, output are explained, and exercises and examples with real data are included.
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.
Using formal descriptions, graphical illustrations, practical examples, and R software tools, Introduction to Multivariate Statistical Analysis in Chemometrics presents simple yet thorough explanations of the most important multivariate statistical methods for analyzing chemical data. It includes discussions of various statistical methods, such as principal component analysis, regression analysis, classification methods, and clustering. Written by a chemometrician and a statistician, the book reflects the practical approach of chemometrics and the more formally oriented one of statistics. To enable a better understanding of the statistical methods, the authors apply them to real data examples from chemistry. They also examine results of the different methods, comparing traditional approaches with their robust counterparts. In addition, the authors use the freely available R package to implement methods, encouraging readers to go through the examples and adapt the procedures to their own problems. Focusing on the practicality of the methods and the validity of the results, this book offers concise mathematical descriptions of many multivariate methods and employs graphical schemes to visualize key concepts. It effectively imparts a basic understanding of how to apply statistical methods to multivariate scientific data.
Research Paper (postgraduate) from the year 2015 in the subject Medicine - Other, grade: II Level Master, University of Pavia (Unit of Medical and Genomic Statistics), course: Medical and Genomic Statistics, language: English, abstract: Electroencephalography, commonly called 'EEG', estimates through the application of electrodes, the electrical activity of the brain (which is the sum of the electrical activity of each neuron). In recent years, with the goal of making more reliable the EEG, many researchers have turned their interest in the development of tools, methods and software. This thesis describes some best procedures for the experimental design, data visualization and descriptive or inferential statistical analysis. The application of statistical models to single or multiple subjects study-design are also described, including parametric and non-parametric approaches. Methods for processing multivariate data (PCA, ICA, clustering) were described. Re-sampling methods (bootstrap) using many randomly software-generated samples were also described. The aim of this work is to provide, with statistical concepts and examples, information on the qualitative and quantitative approaches related to the electroencephalographic signals. The work consists into three parts: INTRODUTION TO ELECTROENCEPHALOGRAPHY (GENERAL CHARACTERISTICS); DATA MINING AND STATISTICAL ANALYSIS; EXPERIMENTAL STUDY DESIGNS. The six works included in the section called “EXPERIMENTAL STUDY DESIGNS” analyze EEG alterations in the protocols: Electrocortical activity in dancers and non-dancers listening to different music genre and during imaginative dance motor activity; Electrocortical activity during monosynaptic reflex in athletes; Monitoring of electrocortical activity for evaluation of seasickness; Electrocortical activity in different body positions; Electrocortical activity in athletes and non-athletes during body balance tasks; Electrocortical responses in volunteers with and without specific experience watching movies including the execution of complex motor gestures. In the section called “OTHER INTERESTING THINGS” were included one work that analyze EMG (electromyography) alterations in pathological and healthy subjects in the protocol: Comparison between clinical diagnostic criteria of sleep bruxism and those provided by a validated portable holter. The described procedures can be used for clinical trials, although the studies proposed in this work do not refer to samples from pathological subjects. With its multi-specialist approach, through many theoretical and practical feedback, this work will be useful for specializing in neuroscience, statistics, engineering or physiology.
Physical anthropologists, like other research workers, are recognizing that the standard multivariate statistical techniques of recent decades are in need of refinement and greater precision. Increasingly it is felt that more sophisticated methods are called for, specifically designed for the materials and problems at issue. To this end the editors were asked by organizers of the First Intercongress of the International Union of Anthropological and Ethnological Sciences to develop a symposium on this general subject. With the title of this book, the symposium was held in Amsterdam on April 23-25, 1981. Invited were mathematical statisticians who were known to have an acquaintance with and interest in anthropological problems, together with anthropologists and human geneticists who consider multivariate methodology essential for their research. This volume constitutes an updated and revised selection from among the papers presented, together with a few supplementary papers by authors who were not present but whose work fills out the intended coverage and makes the volume more complete with respect to the state of affairs in the field. The papers are devoted both to new methodology and to its practical application. Mathematical statisticians may wish to know more about the biological nature and the kinds of materials and samples on which mathematical thinking can be exercised. Anthropologists as practitioners may not be fully aware of the possibilities and limitations in particular mathematical models and methods. Our purpose has been to bring the two groups together, for personal discussions across disciplinary lines as well as within disciplines.