Multivariate Analysis (ΣΕΕ6)
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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. |
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| General Competences |
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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) | ||||||||||
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| Use of Information and Communications Technology |
Use of ICT in communication with students | ||||||||||
| Teaching Methods |
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| 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.