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Multivariate Statistics [MA4472] 
Sommersemester 2020
Zentrum Mathematik
Zuordnungen: 1 
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The focus of the course is on understanding the foundations and principles underlying the analysis of multivariate data of moderate dimensions. The need to handle large amounts of multivariate data and analyze for either summarization or prediction arises in most scientific fields, including genetics, genomics, psychology, sociology, finance, insurance and engineering. Sensible multivariate analysis and the ability to generalize to high-dimensional datasets relies on a firm foundation in the theory underlying multivariate testing and modelling. The course begins with definitions and properties of the multivariate Normal, spherical and Wishart distributions. It then moves to the Hotelling T² and Lambda statistics for measuring differences among mean vectors. It ends with coverage of multivariate analysis of variance (MANOVA), a special case of multivariate regresssion, also to be covered as time permits.
MA1101, MA1102, MA1401, MA2402, MA4401, multiple integration and basic knowledge of the R package
At the end of the course students are able to characterize multivariate Normal and Wishart distributions, and prove theorems concerning the distributions of derived variables and multivariate test statistics. The students will have gained skills in rigorous statistical theory proof development, which would enable them to prove many of the theorems they had encountered in prior statistical courses, such as Linear Models and Introduction to Statistics. They will have further practice in the application of techniques learned in Linear and Matrix Algebra, such as principal component analysis.
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[1] Fujikoshi, Y., Ulyanov, V.V. and Shimizu, R. (2010). Multivariate Statistics, Wiley
[2] Izenman, A.J. (2008). Modern Multivariate Statistical Techniques, Springer.
[3] Johnson, R.A., Wichern, D.W. (2007). Applied Multivariate Statistical Analysis, Pearson.
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