SUBJECT

Title

Multivariate statistical methods

Type of instruction

lecture

Level

master

Faculty

Faculty of Science

Part of degree program

Mathematics MSc

Credits

Recommended in

Semesters 1-4

Typically offered in

Autumn/Spring semester

Course description

Estimation of the parameters of multidimensional normal distribution. Matrix valued distributions. Wishart distribution: density function, determinant, expected value of its inverse.

Hypothesis testing for the parameters of multivariate normal distribution. Independence, goodness-of-fit test for normality. Linear regression.

Correlation, maximal correlation, partial correlation, kanonical correlation.

Principal component analysis, factor analysis, analysis of variances.

Contingency tables, maximum likelihood estimation in loglinear models. Kullback–Leibler divergence. Linear and exponential families of distributions. Numerical method for determining the L-projection (Csiszár’s method, Darroch–Ratcliff method)

Readings

J. D. Jobson, Applied Multivariate Data Analysis, Vol. I-II. Springer Verlag, 1991, 1992.
C. R. Rao: Linear statistical inference and its applications, Wiley and Sons, 1968,