ECTS credits ECTS credits: 5
ECTS Hours Rules/Memories Student's work ECTS: 85 Hours of tutorials: 5 Expository Class: 15 Interactive Classroom: 20 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
The objective of the course is for the student to have an advanced knowledge of parametric statistical inference techniques.
1. Preliminaries of Mathematical statistics
2. The principle of maximum likelihood
Definition. Asymptotic properties of the maximum likelihood estimator. Optimality. Computational aspects.
3. Unbiased estimation
Uniformly centered estimate of minimum variance. U- statistics.
4. Estimation by confidence regions
Pivotal, asymptotic and Neyman methods. Bootstrap trusted regions.
5. Hypothesis testing
Definitions. Uniformely More Powerful Test: Neyman Pearson's Lemma. Karlin-Rubin. Bilateral tests: focused tests. The likelihood ratio test.
6. Bayes Methods
The Bayesian approach. Bayes estimation. Regions of credibility. Bayesian contrasts.
Basic blibliography
Knight, K. (2000) Mathematical Statistics. Chapman Hall.
Panaretos, V. M. (2016). Statistics for Mathematicians: A Rigurous First Course. Birkhäuser.
Shao (2003) Mathematical Statistics. Springer.
Shao (2005) Mathematical Statistics: Exercises and Solutions. Springer.
Vélez Ibarrola, R. and García Pérez, A. (2012) Principios de Inferencia Estadística. UNED.
Complementary blbilography:
Casella, G. y Berger, R.L. (2002). Statistical Inference. Wadsworth & Brooks/Cole.
Garthwaite, P.H., Jollliffe, I.T. and Jones, B. (2002). Statistical Inference. Prentice Hall
Gómez Villegas, M.A. (2005). Inferencia Estadística. Díaz de Santos
Lehmann, E.L. (1991). Theory of Point Estimation. Second Edition. Wiley.
Lehmann, E.L. (2005). Testing Statistical Hypothesis. Segunda Edition. Wiley.
Pawitan, Y. (2001). In all likelihood. . Oxford University Press.
Wasserman, L. (2005). All of Statistics. Springer.
In this matter the basic, general and transversal competences included in the memory of the title will be worked on. The specific competences that will be promoted in this area are indicated below:
Specific competences:
E1 - Know, identify, model, study and solve complex statistical and operational research problems, in a scientific, technological or professional context, arising from real applications.
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.
The activity at the classroom of the students will be a maximum of 35 hours between expository and interactive teaching. In the expository part, the teaching staff will make use of multimedia presentations, while in the interactive part, the students will solve different questions raised about the contents of the subject.
The students will have, through the virtual campus of the subject, the teaching material (presentations, notes, exercises) of the subject. Throughout the course, works will be proposed that students must solve with the tutor's supervision. This tutoring will be done in small groups
Continuous assessment and a final exam will be evaluated at the first opportunity. The weight of the continuous evaluation will be 50%. The continuous evaluation will consist of the delivery and revision of different works proposed throughout the course. The exercises will be of different levels of theoretical / practical difficulty
Thus, the most advanced will allow evaluating the acquisition of skills CB6, CB7, CG4, CT1, E3 and E4.
More applied exercises will be presented that will allow modeling complex situations, developing skills CB8, CG1, CG5, CT2, E1, E5, E6.
Autonomy will be valued in the resolution of proposals, as specified in competencies CB10, E8.
The final grade will be the weighted average of the continuous evaluation of the first part of the subject and the final exam. The weights will be 30% and 70% respectively.
It is considered that the personal work time of the students to pass the subject is 125 hours distributed as follows:
1) On-site activity (35):
2) Study of the material (35): It is estimated 1 hour for each hour of activity
3) Continuous assessment work (55 hours)
To successfully pass the subject, it is advisable to attend the expository and interactive teaching sessions, with daily monitoring of the work carried out in the classroom being essential. Likewise, it is recommended that the student have prior knowledge of probability calculation, and a good command of abstract mathematical concepts.
The development of the contents of the subject will be carried out taking into account that the competences to be acquired by the students must meet the MECES3 level. The contents included in this subject are advanced contents, which delve into the idea and construction, as well as the theoretical justification, of the usual proposals for estimators and contrast methods, allowing students to acquire a solid foundation on the foundations of inferential statistics .
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.
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
Coordinador/a- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- alberto.rodriguez.casal [at] usc.es
- Category
- Professor: University Professor
| 01.17.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 04 |
| 06.26.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 04 |