ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Student's work ECTS: 99 Hours of tutorials: 3 Expository Class: 24 Interactive Classroom: 24 Total: 150
Use languages Spanish, Galician
Type: Ordinary Degree Subject 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
To introduce the main principles of Statistical Inference, and the basic techniques related to the Linear Model.
Chapter 1. Nonparametric inference nased on the empirical distribution function (3 hours)
Empirical distribution function. Kolmogorov-Smirnov test. Lilliefors test. Density estimation.
Chapter 2. Ji-squared tests (2 hours)
Goodness of fit test. Indepence test. Homogeneity test.
Chapter 3. Point estimation. (5 hours)
Parametric methods of estimation: method of moments and maximum likelihood. Bounds for the variance: Frechet-Cramer-Rao inequality.
Chapter 4. Parametric confidence regions. (3 hours)
Confidence intervals methods: pivotal method, Neyman’s method, Bayesian confidence intervals and asymptotic intervals.
Chapter 5. Parametric hypothesis testing. (5 hours)
Optimality criteria between hypothesis tests. Neyman-Pearson test. Likelihood ratio test.
6. The linear regression model (7 hours)
The simple linear regression model. The least squares method. Formulation of the multiple linear regression model. Solution in the context of the general linear model: matrix notation, least squares estimation, properties of the estimators, inference on parameters, prediction. Interpretation of coefficients in multiple regression: the confounding phenomenon.
7. Validation of a linear regression model (3 hours).
Variability decomposition. The coefficient of determination. Simple, multiple and partial correlation. Variable selection methods. Model validation. Pre-regression transformations.
BASIC BIBLIOGRAPHY:
Faraway, J.J. (2004). Linear models with R. Chapman and Hall. Tamén dispoñible en http://www.utstat.toronto.edu/~brunner/books/LinearModelsWithR.pdf
Panaretos, V. M. (2016). Statistics for Mathematicians: A Rigurous First Course. Birkhäuser. Tamén dispoñible en: https://link.springer.com/content/pdf/10.1007%2F978-3-319-28341-8.pdf
Vélez Ibarrola, R. y García Pérez, A. (1997). Principios de Inferencia Estadística. UNED.
COMPLEMENTARY BIBLIOGRAPHY:
Casella, G. e Berger, R.L. (1990). Statistical Inference. Wadsworth & Brooks/Cole.
Chihara, L. e Hesterberg, T. (2011). Mathematical Statistics with Resampling and R. Wiley.
DeGroot, M.H., Schervish, M.J. (2002). Probability and Statistics. Addison-Wesley, Boston.
García Pérez, A. (2010). Estadística básica con R. UNED.
Ross, S. (2007). Introducción a la Estadística. Reverté S.A., Barcelona.
Peña, D. (2002). Regresión y diseño de experimentos. Alianza Editorial.
Sheather, S.J. (2009). A modern approach to regression with R. Springer.
In this course the competences indicated in the memory of the Degree in Mathematics with the codes CB2, CB3, CB4, CG3, CT3, CE1, CE7 and CE9 will be worked.
The general and specific skills that will be enhanced in Statistical Inference are indicated below.
General competences:
[CG3] Apply both the theoretical-practical knowledge acquired and the capacity for analysis and abstraction in the definition and formulation of problems and in the search for their solutions in both academic and professional contexts.
Specific competences:
[CE1] Understand and use mathematical language.
[SC7] Propose, analyze, validate and interpret models of simple real situations, using the most appropriate mathematical tools for the purposes pursued.
[SC9] Use computer applications of statistical analysis, numerical and symbolic calculation, graphic visualization, optimization and scientific software, in general, to experiment in Mathematics and solve problems.
The expository and interactive teaching will be face-to-face, adjusting the distribution agreed by the Faculty of Mathematics, and will be complemented with the Virtual Campus of the subject, where students will find bibliographic material, problem bulletins, practice scripts, etc. Through the Virtual Campus, students will also be able to take tests and submit continuous assessment work, as described in the corresponding section. Tutorials can be face-to-face, via e-mail or the institutional software MS Teams.
The grade will be the maximum between the final exam grade and the grade obtained taking into account the continuous evaluation. In the latter case, the weight of the continuous assessment will be 30% of the final grade and the exam the other 70%.
The continuous evaluation will allow us to verify that the CG3, CE1, CE7 and CE9 competencies of the Degree verification report are acquired. It will be based mainly on practical activities. The continuous evaluation will consist of two tests that will be carried out in the Computer Classes and will deal with content seen throughout the laboratory sessions, and one of a more theoretical-practical nature that will be carried out in the seminar session. The number and format of the tests will be common to both expository groups.
The final exam, which will be common to both groups, will consist of a theoretical part based on concepts or short questions in which it is intended to evaluate the acquisition of the fundamental knowledge of the subject. The rest of the exam will consist of a practical part focused on the resolution of exercises and problems similar to those proposed throughout the course, where the acquisition of competences CE7 and CE9 will be evaluated.
The assessment system in the second opportunity will be identical to that of the first opportunity. In addition, it will be considered that the student took the evaluation when he/she takes the final exam.
Individual work is about one hour and a half for each hour of teaching, including preparation of the assignments.
It is recommended to attend lectures, seminars, computer labs , as well as the proposed activities, as fundamental means to take advantage of the course.
In order to successfully pass the course, it is also advisable to follow the proposed work plans. It is also recommended that the student practices the use of the statistical package R to explore the possibilities of the different techniques explained throughout the course.
R software, which will be the basic tool in computer labs, can be freely downloaded from http://www.r-project.org/.
Online moodle-based platform “Campus Virtual” will be used.
Wenceslao Gonzalez Manteiga
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- Phone
- 881813204
- wenceslao.gonzalez [at] usc.es
- Category
- Professor: University Professor
Alberto Rodriguez Casal
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- alberto.rodriguez.casal [at] usc.es
- Category
- Professor: University Professor
Mercedes Conde Amboage
Coordinador/a- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- mercedes.amboage [at] usc.es
- Category
- Professor: Temporary PhD professor
Maria Alonso Pena
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- mariaalonso.pena [at] usc.es
- Category
- Professor: Intern Assistant LOSU
| Tuesday | |||
|---|---|---|---|
| 10:00-11:00 | Grupo /CLE_02 | Spanish | Classroom 06 |
| 12:00-13:00 | Grupo /CLIS_01 | Galician, Spanish | Classroom 03 |
| 13:00-14:00 | Grupo /CLIS_02 | Galician, Spanish | Classroom 09 |
| Wednesday | |||
| 09:00-10:00 | Grupo /CLIL_05 | Spanish | Computer room 3 |
| 10:00-11:00 | Grupo /CLE_01 | Galician, Spanish | Classroom 03 |
| 10:00-11:00 | Grupo /CLIL_04 | Spanish | Computer room 2 |
| 11:00-12:00 | Grupo /CLIL_06 | Spanish | Computer room 3 |
| Thursday | |||
| 09:00-10:00 | Grupo /CLIS_03 | Spanish | Classroom 06 |
| 09:00-10:00 | Grupo /CLIL_02 | Spanish, Galician | Computer room 2 |
| 10:00-11:00 | Grupo /CLIS_04 | Spanish | Classroom 06 |
| 10:00-11:00 | Grupo /CLIL_03 | Galician, Spanish | Computer room 3 |
| 11:00-12:00 | Grupo /CLIL_01 | Galician, Spanish | Computer room 3 |
| 05.30.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 06 |
| 06.30.2025 10:00-14:00 | Grupo /CLE_01 | Classroom 06 |