Multivariate Statistical Analysis I (VL)
 Kategorie
 Master
 Lehrende(r)
 A. Andriyashin, R. Timofeev
Course Outline
Multivariate statistical analysis (MVA) describes a collection of procedures which involve observation and analysis of more than one statistical variable at a time. There are many different models, each with its own type of analysis:
 Regression analysis attempts to determine a linear formula that can describe how some variables respond to changes in others. Linear regression is a method for determining the parameters of a linear system, that is a system that can be expressed as follows: In MVA course a case of multiple linear regression is studied, when there are more than one explanatory variable.

Multivariate normal distribution, also sometimes called a multivariate Gaussian distribution, is a specific probability distribution, which is a generalization to higher dimensions of the onedimensional normal distribution:
 Principal components analysis attempts to determine a smaller set of synthetic variables that could explain the original set. PCA is an orthogonal linear transformation that transforms the data to a new coordinate system such that the greatest variance by any projection of the data comes to lie on the first coordinate (called the first principal component), the second greatest variance on the second coordinate, and so on. PCA can be used for dimensionality reduction in a data set while retaining those characteristics of the data set that contribute most to its variance, by keeping lowerorder principal components and ignoring higherorder ones.
 Linear discriminant analysis (LDA) are used in statistics to find the linear combination of features which best separate two or more classes of object or event. LDA approaches the problem by assuming that the probability density functions are normally distributed with identical fullrank covariances. Quadratic discriminant analysis (QDA)is closely related to linear discriminant analysis (LDA). Unlike LDA however, in QDA there is no assumption that the covariance of each of the classes is identical.
 Cluster analysis is the classification of objects into different groups, or more precisely, the partitioning of a data set into subsets (clusters). An important step in any clustering is to select a distance measure, which will determine how the similarity of two elements is calculated. Some common distance functions are the Euclidean distance , the Manhattan distance and the Mahalanobis distance
Literature
 Härdle, Simar (2003) Applied Multivariate Statistical Analysis, Springer Verlag.
 Johnson, Wichern (1998, 4th edition) Applied Multivariate Statistical Analysis, Prentice Hall
 Backhaus, Erichson, Plinke, Weiber (1994, 7. Auflage) Multivariate Analysemethoden, Springer, München, New York
 Mardia, Bibby, Kent (1979) Multivariate Analysis, Academic Press
 Härdle, Klinke, Müller (1999) XploRe  Academic Edition, The Interactive Statistical Computing Environment, Springer, New York