Multivariate Analysis (ΣΕΕ6)

Graduate Courses Outlines - Department of Mathematics

General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Graduate
Course Code	ΣΣΕ6
Semester	2
Course Title	Multivariate Analysis
Independent Teaching Activities	Lectures-Laboratory (Weekly Teaching Hours: 3, Credits: 7.5)
Course Type	Specialized general knowledge
Prerequisite Courses	-
Language of Instruction and Examinations	Greek
Is the Course Offered to Erasmus Students	Yes (in English)
Course Website (URL)	See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes

The aim of the course is to present techniques and methods of Multivariate Statistical Analysis. The interest is initially focused on the study of multivariate distributions and, in particular, the multivariate normal distribution that predominates in the classical multivariate analysis. Estimation techniques and statistical tests on the parameters of the multivariate normal distribution are presented and studied. Afterwards the following subjects are presented: Principal Components, Discriminant Analysis and Cluster Analysis. The above methods are presented and studied theoretically. Their implementation is provided by the use of appropriate statistical software. Upon completing the course students should be able to elaborate research issues on Multivariate Statistical Analysis. They also should be able to apply the aforementioned multivariate techniques in a real data set.

General Competences

Working independently Decision-making Production of free, creative and inductive thinking Criticism and self-criticism

Syllabus

The multivariate normal distribution. The non-central chi-square and F distributions. Quadratic forms: Independence, distributions. Spherical and Elliptical distributions. Maximum likelihood estimators (m.l.e) of the parameters of the multivariate normal distribution. Classical properties of m.l.e. The Wishart distribution. Tests of hypotheses of mean vectors. Likelihood ratio method - Union/Intersection method. Hotelling's T2 statistic and distribution. One-way MANOVA. Tests concerning variance-covariance matrices. Tests of independence. Principal Components. Discriminant Analysis. Cluster Analysis

Teaching and Learning Methods - Evaluation

Delivery	Classroom (face-to-face)
Use of Information and Communications Technology	Use of ICT in communication with students
Teaching Methods	Activity Semester Workload Lectures 39 Working independently 78 Exercises-Homework 70.5 Course total 187.5
Student Performance Evaluation	Final written exam in Greek (in case of Erasmus students in English).

Attached Bibliography

• Anderson, T. W. (2003). An Introduction to Multivariate Statistical Analysis. 3rd Edition. Wiley.
• Fang, K.T., and Zhang, Y.T.. (1990). Generalized Multivariate Analysis. Springer. Berlin.
• Flury, B. (1997). A first course in multivariate statistics. Springer.
• Johnson, R. A. and Wichern, D. W. (2006). Applied Multivariate Statistical Analysis. Prentice Hall.
• Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979). Multivariate Analysis. Academic Press.
• Muirhead, R. J. (1982). Aspects of Multivariate Statistical Theory. Wiley.
• Rencher, A. C. (1995). Methods of Multivariate Analysis. Wiley.
• Srivastava, M. S. (2002). Methods of multivariate statistics. Wiley.