Multivariate Analysis (Probability and Mathematical Statistics)

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.

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.