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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Chapter 2Basic Properties of Random Vectors
Chapter 3Normal Distribution Theory
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allocation asymptotic canonical correlation canonical correlation analysis clusters columns confidence intervals configuration Consider Corollary correlation matrix corresponding covariance matrix data matrix defined degrees of freedom denote density diagonal dimensions discriminant rule distance matrix eigenvalues eigenvectors elements endogenous variables equal equation Euclidean Example Exercise factor analysis given gives groups Hence independent instrumental variables least squares likelihood function likelihood ratio linear combination Mahalanobis distance Mardia maximized mean vector measure method multinomial distribution multivariate non-singular non-zero eigenvalues normal distribution Note null hypothesis orthogonal orthogonal matrix p-vector parameters partition points population principal component analysis problem Proof random sample random vector rank regression rejected represents respectively result ri ri rows sample mean scores Section solution SSP matrix sum of squares Suppose symmetric symmetric matrix Table Theorem tion transformation uncorrelated union intersection univariate variance Wishart distribution zero