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.
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Multivariate Analysis deals with observations on more than one variable where there is some inherent interdependence between variables. Most available books on the subject concentrate on either the theoretical or the data analytic approach. This book not only combines theses two approaches but also emphasizes modern developments, so, although primarily designed as a textbook for final year undergraduates and postgraduate students in mathematics and statistics, certain of the sections will commend themselves to research workers.
Broadly speaking the first half of the book contains direct extensions of univariate ideas and techniques, including exploratory data analysis, distribution theory and problems of inference. The remaining chapters concentrate on specifically multivariate problems which have no meaningful analogues in the univariate case. Topics covered include econometrics, principal component analysis, factor analysis, canonical correlation analysis, discriminate analysis, cluster analysis, multi-dimensional scaling and directional data.
Several new methods of presentation are used, for example, the data matrix is emphasized throughout, and density-free approach is given to normal theory, tests are constructed using the likelihood ratio principle and the union intersection principle, and graphical methods are used in explanation.
The reader is assumed to have a basic knowledge of mathematical statistics at an undergraduate level together with an elementary understanding of linear algebra. There are, however, appendices which provide a sufficient background of matrix algebra, a summary of univariate statistics and some statistical tables.
Broadly speaking the first half of the book contains direct extensions of univariate ideas and techniques, including exploratory data analysis, distribution theory and problems of inference. The remaining chapters concentrate on specifically multivariate problems which have no meaningful analogues in the univariate case. Topics covered include econometrics, principal component analysis, factor analysis, canonical correlation analysis, discriminate analysis, cluster analysis, multi-dimensional scaling and directional data.
Several new methods of presentation are used, for example, the data matrix is emphasized throughout, and density-free approach is given to normal theory, tests are constructed using the likelihood ratio principle and the union intersection principle, and graphical methods are used in explanation.
The reader is assumed to have a basic knowledge of mathematical statistics at an undergraduate level together with an elementary understanding of linear algebra. There are, however, appendices which provide a sufficient background of matrix algebra, a summary of univariate statistics and some statistical tables.
About the Author
Edited by K. V. Mardia
--This text refers to the
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34 of 34 people found the following review helpful:
4.0 out of 5 stars
nice coverage by Mardia and company,
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This review is from: Multivariate Analysis (Probability and Mathematical Statistics) (Paperback)
This book provides an excellent general treatment of multivariate analysis. It uses the geometric approach much more than other texts with the exception of Gnanadesikan's. It is written with elegant style. It does not describe thoroughly the multivariate normal distribution theory that one find in the classic text of Anderson. Anderson takes a much more algebraic approach and concentrates heavily on multivariate normal theory. Matrix algebra is important when studying multivaraite analysis and is particularly important if you want to read and understand Anderson. It is not as critical for this and some of the other. As with many other books on multivariate analysis, factor analysis and structural equation modelling are given little or no coverage even though they are important in applied problems. Specialized books like Harman and Bollen give a detailed treatment of factor analysis and structural equation models respectively. Also this book and many others do not cover the bootstrap methods. The bootstrap plays an important role in multivariate analysis and it is nice to see that at least Anderson gives it some coverage in the second edition of his book. This may in part be due to the fact that he is a Stanford Professor who has seen the efforts of Efron, Tibshirani and Romano on the Stanford campus.
28 of 29 people found the following review helpful:
5.0 out of 5 stars
best book on multivariate analysis,
By
This review is from: Multivariate Analysis (Probability and Mathematical Statistics) (Paperback)
This book gives the clearest and most elegant presentation of the theory of multivariate analysis I have seen. The reader should have a good background in linear algebra before starting this one, but with this background the authors give a very concise treatment of a large area of statistics. Many topics that are not covered in most multivariate analysis texts are covered here. The exercises are also outstanding. Many of them are very difficult and lead to more profound results. I highly recommend this text!
9 of 11 people found the following review helpful:
4.0 out of 5 stars
Excellent if you know some linear algebra,
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This review is from: Multivariate Analysis (Probability and Mathematical Statistics) (Paperback)
A very good book for someone who knows linear algebra. In fact, it is probably a good introduction to advanced statistics for someone with a numerical background.The reason I did not give if 5 is that it has started to show its age and insists that data is best arranged in rows. Those with a numerical background invariably use columns (unless they are doing funky stuff). The description of Principal Component Analysis (PCA) is based on eigendecompositions rather than a singular value decomposition. Apart from being a numerical no-no, it is also a nice description of the data. Every 10-20 years a statistician reinvents a minor variant of PCA (often without obvious knowledge of the previous ones). It would be nice if this was made more explicit. The connection with factor analysis is mentioned (and it has a good chapter of its own), but it would be nice to mention at least the Harkunen-Loeve and Hotelling-transform.
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Inside This Book
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First Sentence:
Multivariate analysis deals with data containing observations on two or more variables each measured on a set of objects. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
pitprop data, canonical correlation variables, normal data matrix, shrew data, discriminant rule allocates, canonical correlation vectors, cork data, centring matrix, union intersection test, equicorrelation matrix, union intersection approach, discarding variables, standardized eigenvectors, multinormal populations, univariate hypotheses, first structural equation, multinormal distribution, multivariate scatter, confidence cone, single linkage cluster analysis, value decomposition theorem, last principal component, spectral decomposition theorem, canonical scores, single linkage method Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Karl Pearson, Cap Gris Nez, Proof First, Proof Write, Sepal Petal New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Multivariate analysis deals with data containing observations on two or more variables each measured on a set of objects. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
pitprop data, canonical correlation variables, normal data matrix, shrew data, discriminant rule allocates, canonical correlation vectors, cork data, centring matrix, union intersection test, equicorrelation matrix, union intersection approach, discarding variables, standardized eigenvectors, multinormal populations, univariate hypotheses, first structural equation, multinormal distribution, multivariate scatter, confidence cone, single linkage cluster analysis, value decomposition theorem, last principal component, spectral decomposition theorem, canonical scores, single linkage method Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Karl Pearson, Cap Gris Nez, Proof First, Proof Write, Sepal Petal New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 39
books:
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100
books
cite this book:
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- Multivariate Analysis: 1st: International Symposium Proceedings by Paruchuri R. Krishnaiah in Back Matter (1), and Back Matter (2)
- Statistical Distributions in Scientific Work: Vol. 1: Models and Structures Vol. 2: Model Building and Model Selection Vol. 3: Characterizations and ... (NATO Science Ser C:). THREE VOLUMES (v. 1) by Ganapati P. Patil in Back Matter (1), and Back Matter (2)
- Cluster Analysis by Brian S. Everitt on page 381, and Back Matter
- Multivariate Analysis (Griffin's Statistical Monographs and Courses) by Maurice George Kendall in Back Matter (1), and Back Matter (2)
- Mathematical Taxonomy (Probability & Mathematical Statistics) by Nicholas Jardine in Back Matter
See all 39 books this book cites
- Applied Multivariate Data Analysis: Volume II: Categorical and Multivariate Methods (Springer Texts in Statistics) by J. D. Jobson on 4 pages
- Multivariate Data Reduction and Discrimination with SAS Software by Ravindra Khattree in Back Matter (1), Back Matter (2), and Back Matter (3)
- Random Data: Analysis & Measurement Procedures by Julius S. Bendat in Back Matter (1), and Back Matter (2)
- Generalized, Linear, and Mixed Models (Wiley Series in Probability and Statistics) by Charles E. McCulloch in Back Matter (1), and Back Matter (2)
- Methods for Meta-Analysis in Medical Research (Wiley Series in Probability and Statistics - Applied Probability and Statistics Section) by Alexander J. Sutton in Back Matter (1), and Back Matter (2)
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