@MISC{Wermuth_multivariatestatistical, author = {Nanny Wermuth}, title = {MULTIVARIATE STATISTICAL ANALYSIS}, year = {} }

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Abstract

Classical multivariate statistical methods concern models, distributions and inference based on the Gaussian distribution. These are the topics in the first textbook for mathematical statisticians by T.W. Anderson that was published in 1958 and that appeared as a slightly expanded 3rd edition in 2003. Matrix theory and notation is used there extensively to efficiently derive properties of the multivariate Gaussian or the Wishart distribution, of principal components, of canonical correlation and discriminant analysis and of the general multivariate linear model in which a Gaussian response vector variable Ya has linear least-squares regression on all components of an explanatory vector variable Yb. In contrast, many methods for analysing sets of observed variables have been developed first within special substantive fields and some or all of the models in a given class were justified in terms of probabilistic and statistical theory much later. Among them are factor analysis, path analysis, structural equation models, and models for which partial-least squares estimation have been proposed. Other multivariate techniques such as cluster analysis and multidimensional scaling have