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 Spanish, Galician
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: First Semester
Teaching: With teaching
Enrolment: Enrollable
It is intended that the student become familiar with statistical problems where functional data may appear and acquire the necessary skills to deal with them. For this, the main statistical techniques will be covered, relating the known techniques in the multivariate or time series environment to the specificities in the application to functional data.
The objectives to be achieved as a result of learning are:
• Be able to identify and model problems with functional data in real applications.
• Know the appropriate software to solve this type of problem.
• Understand the implications of the hypotheses in the results of the models and their possible reformulations.
• Know how to interpret the results for their presentation in highly multidisciplinary environments, both before specialized and non-specialized audiences.
Unit 1. Concepts of Functional Analysis useful for Functional Data.
Unit 2. Introduction. First steps. Representation and transformations of Functional Data.
Unit 3. Exploratory analysis of functional data. Summary statistics. Depth measurements.
Unit 4. Regression with functional data: Scalar response, functional response, median estimate and conditional quantile, ANOVA.
Unit 4. Supervised and unsupervised classification techniques.
Unit 5. Hypothesis testing with functional data.
Basic
• Ferraty, F. And Vieu, Ph. (2006). Nonparametric Modelling for Functional Data. Springer.
• Ramsay, J.O. and Silverman, B.W. (2005) Functional Data Analysis. 2nd Edition. Springer
• Ramsay, J.O. and Silverman, B.W. (2002) Applied Functional Data Analysis. Springer
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• Bosq, D. (2000). Linear processes in function spaces. Springer
• Cardot, H. (2000). Nonparametric estimation of smoothed principal component analysis of sampled noisy functions. Journal of Nonparametric Statistics, Vol.12, 503-538.
• Cardot, H., Ferraty, F. and Sarda, P. (2003). Spline estimators for the functional linear model. Statistica Sinica, 13, 571-591.
• Cuevas, A., Febrero, M. and Fraiman, R. (2002). Linear functional regression: The case of fixed design and functional response. The Canadian Journal of Statistics, 30, 285-300.
• Febrero-Bande M, Oviedo de la Fuente M (2012). “Statistical Computing in Functional Data Analysis: The R Package fda.usc.” Journal of Statistical Software, 51(4), 1–28. http://www.jstatsoft.org/v51/i04/.
• Ferraty, F. and Vieu, Ph.(2001) The functional nonparametric model and its applications to spectrometric data. Computational Statistics, 17, 545-564.
• James, G.M. and Hastie, T.J. (2001) Functional linear discriminant analysis for irregularly sampled curves. Journal of the Royal Statistical Society, Series B, 63, 533-550.
The specific competences that will be promoted are indicated below:
E1 - Know, identify, model, study and solve complex statistical and operational research problems, in a scientific, technological or professional context, arising from real applications.
E2 - Develop autonomy for the practical resolution of complex problems arising in real applications and for the interpretation of results in order to aid decision-making.
E3 - Acquire advanced knowledge of the theoretical foundations underlying the different methodologies of statistics and operational research, which allow their specialized professional development.
E4 - Acquire the necessary skills in the theoretical-practical management of probability theory and random variables that allow their professional development in the scientific / academic, technological or specialized and multidisciplinary professional field.
E5 - To deepen the knowledge in the specialized theoretical-practical foundations of modeling and study of different types of dependency relationships between statistical variables.
E6 - Acquire advanced theoretical-practical knowledge of different mathematical techniques, specifically oriented to aid in decision-making, and develop reflective capacity to evaluate and decide between different perspectives in complex contexts.
E8 - Acquire advanced theoretical-practical knowledge of techniques for making inferences and contrasts related to variables and parameters of a statistical model, and know how to apply them with sufficient autonomy in a scientific, technological or professional context.
E10 - Acquire advanced knowledge on methodologies for obtaining and processing data from different sources, such as surveys, the Internet, or "cloud" environments.
The teaching will consist of exhibition and interactive classes, as well as the tutoring of the learning and the tasks entrusted to the students. In the exhibition and interactive classes, examples will be solved using specialized software, so it is convenient for students to have a computer in the classroom.
Activities will be proposed for the students, which will consist of solving questions, exercises and examples related to the modeling and resolution of functional data problems.
The appropriate support material will be provided to the student through the Master's web server.
The final grade will be a maximum of two: the continuous assessment grade and the final test grade. The continuous evaluation will consist of the delivery of one or several works proposed throughout the course and delivered before the date of the final test. The final test will consist of solving by computer one or more functional data problems with data provided by the teacher that must be solved using the software used during the practical classes.
Both the continuous assessment and the final test are designed to cover all the skills to be developed in the subject.
In cases of fraudulent performance of exercises or tests, the provisions of the respective regulations of the universities participating in the Master in Statistical Techniques will apply.
Each ECTS credit translates into 7 classroom hours. It is estimated that the student will need, for each hour of face-to-face class, an additional hour for the global understanding of the contents. In addition, the continuous assessment work will amount to 10 hours per ECTS credit. In total 25 hours per ECTS credit will result.
1394/5000
Students should have a basic knowledge of exploratory and regression statistical methods, both linear and non-parametric. It is also recommended to have some basic computer skills, and specifically the R software that will be used together with the fda.usc library in practical classes.
It is advisable to actively participate in the learning process of the subject: attendance and participation in the theoretical, practical and computer classes, use of hours of tutoring and the realization of a responsible effort of work and personal assimilation of the studied methods.
RESOURCES FOR LEARNING
Bibliography, free software (R-project.org) and support material provided through the website of the Master in Statistical Techniques.
This guide and the criteria and methodologies described therein are subject to modifications arising from regulations and directives of the universities participating in the Master in Statistical Techniques.
Manuel Febrero Bande
Coordinador/a- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- Phone
- 881813187
- manuel.febrero [at] usc.es
- Category
- Professor: University Professor
| 01.22.2025 10:00-14:00 | Grupo /CLE_01 | Classroom 04 |
| 06.27.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 04 |