Multivariate Statistics

(=Multivariate Statistics I)

Contents:

When conducting empirical statistical studies in medicine, marketing, social sciences etc. researchers are typically recording a multitude of variables and not one variable only. Insofar these surveys deal with multivariate data and random vectors. It is the task of the statistician to determine and investigate the joint distribution of all these variables, to estimate their characteristics (such as expectation vectors, covariance matrices, correlation matrices), and to detect and describe eventual depende ncies between variables in the form of multiple regressions, canonical variables or principal factors. In areas such as marketing (biology, psychology) it may also be interesting to look for homogeneous clusters or 'types' of consumers (bacteria, persons) which are separately investigated or analyzed later on, and to find rules for assigning new objects to these clusters (discrimination, classification, pattern recognition).

The design of suitable statistical methods is conducted in the framework of 'Multivariate Statistics'. This course presents the following topics:

  1. Random vectors and multivariate distributions
  2. Stochastic dependence, regression, and correlation
  3. Empirical principal component analysis, factor analysis, correspondence analysis
  4. Multidimensional scaling (for dissimilarity matrices)
  5. Canonical correlation and corresponding matrix theorems
  6. Classification: discrimination, pattern recognition and cluster analysis
  7. Estimation of parameters (e.g., for multivariate normal distributions), efficiency and optimality of estimators
  8. Wishart distribution, Hotelling s Tē and other distributions
  9. Multivariate test procedures: construction of tests and their properties
Literature:

ANDERSON, T.W.: An introduction to multivariate statistical analysis. Wiley, New York, 1958, 1984.

FAHRMEIR, L., HAMERLE, A., G. Tutz (Hrsg.): Multivariate statistische Verfahren. de Gruyter, Berlin, 1996, 796 pp.

GIFI, A.: Nonlinear multivariate analysis. Wiley, New York, 1990.

GIRI, N.C.: Multivariate statistical inference. Academic Press, New York, 1977.

MARDIA, K.V., KENT, J.T., BIBBY, J.M.: Multivariate analysis. Academic Press, New York, 1979.

SEBER, G.A.F.: Multivariate observations. Wiley, New York, 1984.

Basic knowledge in probability and statistics is recommended for attending this course.