Elements of Multivariate Statistics
Cod: 21163
Department: DCET
Scientific area: Mathematics
Total working hours: 156
Total contact time: 26

In real situations, there is often a need to study simultaneously several characteristics (variables) of individuals of a population. In this course unit we start with an introduction to statistical methods for analysis of multivariate data and proceed with an approach to methods of statistical inference such as hypothesis testing and multivariate confidence regions as well as to some description techniques of multivariate data.

1. Multivariate Data
2. Multivariate Gaussian Distribution
3. Sampling distributions
4. Confidence intervals and multivariate tests

In the end students are expected to be able to fully characterize a multivariate normal distribution. They should also be able to generalize acquired knowledge on univariate and multivariate tests between two or more median vectors (MANOVA) and equality tests between matrices of variance/covariance. Students are also expected to develop skills to calculate multivariate confidence regions and to be able to identify methods of multivariate descriptive statistics appropriate to given situations.

• Multivariate Statistics and Multivariate populations: concepts and examples.
• Multivariate random variables. Linear combinations of random variables. Properties of the matrices of variance/covariance.
• Multivariate normal distribution. Maximum likelihood estimators.
• Sampling distributions.
• Tests of Multivariate Hypotheses. Multivariate Confidence Regions.
• Comparison between two vectors of means. MANOVA test (comparison of median vectors k). Test for equality of matrices of variance/covariance.

Compulsory Reading:
Reis, Elizabeth, Estatística Multivariada Aplicada, Ed. Sílabo.

Complementary Reading (Optional):
Jonhson, R. A. &Wichern, D. W., (2002) Applied Multivariate Statistical Analysis, Prentice-Hall.


Continuous assessment is privileged: 2 or 3 digital written documents (e-folios) during the semester (40%) and a presence-based final exam (p-folio) in the end of the semester (60%). In due time, students can alternatively choose to perform one final presence-based exam (100%).

Students are recommended to have knowledge in the subjects of Linear Algebra (UC 21002 Linear Algebra I) and Applied Statistics (UC 21041 Applied Statistics I).