ECTS credits ECTS credits: 5
ECTS Hours Rules/Memories Student's work ECTS: 85 Hours of tutorials: 5 Expository Class: 20 Interactive Classroom: 15 Total: 125
Use languages Galician (100.00%)
Type: Ordinary subject Master’s Degree RD 1393/2007 - 822/2021
Departments: Statistics, Mathematical Analysis and Optimisation
Areas: Statistics and Operations Research
Center Faculty of Mathematics
Call: Second Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
The aim of this course is to provide students with a knowledge of the basic concepts underlying the most important multivariate techniques, through the use the statistical methodology and software packages for the analysis of multivariate data.
1. Introduction to multivariate analysis.
Basic concepts in matrix algebra for multivariate statistics. Multivariate data: data matrix, mean vector, covariance matrix and correlation matrix. Proximity measures. Graphical representation.
2. Statistical inference for multivariate normal data.
Inference for the mean and the covariance matrix of a normal population. Confidence regions and simultaneous inference. Comparison of multivariate normal populations. Multivariate Normality Testing.
3. Multivariate analysis of variance.
One-way MANOVA. MANOVA table, hypothesis testing, multiple comparisons. Two-way MANOVA. Interaction effect.
4. Principal components analysis.
Decomposition of a random vector in its principal components. Properties and interpretation. Number of components to choose. Biplot.
5. Correspondence analysis.
Expression of the chi-square statistic by the row and column profiles. Extraction of components. Simultaneous representation of rows and columns. Interpretations.
6. Fundamentals of Discriminant Analysis.
Basic concepts. Disciminant analysis with two populations. Discriminant analysis for normal data. Generalization to more than two populations. Logistic discrimination.
7. Cluster analysis.
Hierarchical clustering. Partitioning methods: k-means method.
Basic pibliography
Everitt, B.S. (2005). An R and S-Plus companion to multivariate analysis. Springer.
Hardle, W.K., Simar, L. (2015). Applied multivariate statistical analysis. Fourth Edition. Springer.
Johnson, R.A., Wichern, D.W. (2007). Applied multivariate statistical analysis. Pearson Education.
Mardia, K.V., Kent, J.T., Bibby, J.M. (1979). Multivariate analysis. Academic Press.
Complementary bibliography
Everitt, B.S., Dunn, G. (2001). Applied multivariate data analysis. Hodder Education.
Hastie, T., Tibshirani, R., Friedman, J. (2009). The elements of statistical learning. Springer.
Koch, I. (2014). Analysis of multivariate and high-dimensional data. Cambridge.
Peña, D. (2002). Análisis de datos multivariantes. McGraw-Hill.
Pérez, C. (2004). Técnicas de análisis multivariante de datos. Pearson Educación, S.A.
Seber, G.A.F. (1984). Multivariate observations. Wiley.
In this course the basic, general and multidisciplinary competences given in the global report of the Master on Statistical Techniques will be developed. Specific competences specially strengthened in this course of Multivariate Analysis are E1, E2, E3, E4, E5, E6, E8, E9.
The students will have to attend 35 hours of lectures/interative lessons, in two-hours sesions. During the lectures, the professors will use presentations, whereas in the interactive part, the students will solve some questions and problems using R.
The students will have access to different teaching material (presentations, handouts, assignments) prepared for the course through the USC Virtual Campus. During the course, some individual and group work assignments will be proposed and solved under the professors supervision. This supervision will be done both by virtual (mainly by collaboration apps or e-mail) and presential means in reduced groups.
Continuous assessment (30%): continuous assessment will be based on the solution of exercises where the students will use R and will write a report. With the different tasks that will be proposed during the course, the level of basic competences CB7-CB9 and general competences CG1-CG5, will be assessed. Also the level of multidisciplinary competences CT1-CT5 and specific competences CE1, CE2, CE5, CE6 and CE9 will be assessed.
Final exam (70%): the final exam will include some theoretical and practical questions on the subject contents. With the final exam, specific competences CE1-CE6 will be assessed.
The continuous assessment grade will be preserved along the academic year. In the second opportunity (July), there will be a final exam and the final grade will be the maximum of three quantities: ordinary opportunity grade, final exam grade or weighted average of continuous assessment (30%) and final exam (70%).
The study time and individual work of the students in orde to pass the course is 125 hours, distributed as follows:
1) Presential work (38 hours): 35 hours (lectures-interactive) + 3 hours (exam)
2) Non presential work (87 hours): 1 hours for each lecture-interactive hour (excluding the exam) and time for continuous assessment assignments.
The students should attend both the lectures and the interactive sesions. A daily track of the course contents is crucial for passing the course. The students should also practice with R, in order to explore all the possiblities of the different multivariate techniques explained during the course.
The development of the course contents will be carried out taking into account that the competencies to be acquired by the students must meet the MECES3 level. Emphasis will be placed on the technical foundations of the multivariate tools studied, and they will be applied in different practical examples, so that students become familiar with both the potentialities and possible limitations of the methods.
In cases of fraudulent completion of exercises or tests, the provisions of the respective regulations of the universities participating in the Master's Degree in Statistical Techniques will apply.
This guide and the criteria and methodologies described herein are subject to modifications resulting from regulations and guidelines of the universities participating in the Master's Degree in Statistical Techniques.
Beatriz Pateiro Lopez
Coordinador/a- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- Phone
- 881813185
- Category
- Professor: University Lecturer
| Teacher | Language |
|---|---|
| PATEIRO LOPEZ, BEATRIZ | Galician |
| Teacher | Language |
|---|---|
| PATEIRO LOPEZ, BEATRIZ | Galician |
| Teacher | Language |
|---|---|
| PATEIRO LOPEZ, BEATRIZ | Galician |
| Teacher | Language |
|---|---|
| PATEIRO LOPEZ, BEATRIZ | Galician |