ASYMPTOTIC STATISTICS
| Title | ΑΣΥΜΠΤΩΤΙΚΗ ΣΤΑΤΙΣΤΙΚΗ / ASYMPTOTIC STATISTICS |
| Code | ΣΜΥ014 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter/Spring |
| Coordinator | Georgios Afendras |
| Common | Yes |
| Status | Active |
| Course ID | 600025949 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn (2025-2030)
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| STATISTIKĪ, MONTELOPOIĪSĪ KAI YPOLOGISTIKES METHODOI | Elective Courses belonging to the selected specialization | Spring | - | 10 |
| Academic Year | 2025 – 2026 |
| Class Period | Spring |
| Faculty Instructors | |
| Weekly Hours | 3 |
| Total Hours | 39 |
| Class ID | 600268432
|
Type Of Offer
- Disciplinary Course
Course Type 2021
Specific Foundation
Course Type 2016-2020
- Scientific Area
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600268432
- eLearning: https://elearning.auth.gr/course/view.php?id=9913
Language of Instruction
- Greek (Instruction, Examination)
Prerequisites
General Prerequisites
General Background on Probability Theory and Statistics at the level of undergraduate course
Learning Outcomes
Upon successful completion of the course, the students will:
1. have acquired the knowledge of basic concepts of stochastic convergences,
2. be able to handle limit theorems (laws of large numbers, central limit theorems, Delta method, etc.),
3. have acquired knowledge of the basic statistical functions as well as their asymptotic distribution,
4. be able to derive asymptotic parametric/non-parametric statistical inference.
General Competences
- Apply knowledge in practice
- Retrieve, analyse and synthesise data and information, with the use of necessary technologies
- Make decisions
- Work autonomously
- Work in teams
- Work in an interdisciplinary team
- Generate new research ideas
- Be critical and self-critical
- Advance free, creative and causative thinking
Course Content (Syllabus)
Stichastic convergence
Monotonic/dominated convergence
Uniform integrality
Laws of large numbers
Central limit theorems
Delta method
Asymptotic theory of Maximum Likelihood Estimators
Keywords
Stichastic convergence, Limit theorems, Delta method, Maximum Likelihood Estimators
Educational Material Types
- Notes
- Interactive excersises
- Book
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | ✓ | |||
| Fieldwork | 108 | ✓ | |||
| Reading Assigment | 150 | ✓ | |||
| Exams | 3 | ✓ | |||
| Total | 300 |
Student Assessment
Description
Homework/Presentation 60%
Final Examination 40%
Student Assessment methods
- Written Assignment (Formative, Summative)
- Oral Exams (Formative, Summative)
Bibliography
Additional bibliography for study
Anderson, T.W. (1971). The statistical analysis of time series. Wiley, New York.
Billingsley, P. (1995). Probability and Measure, Wiley series in probability and mathematical statistics, 3rd edition. John Wiley, New York.
Casella, G. and Berger, R.L. (2002). Statistical inference. Pacific Grove, CA: Duxbury.
DasGupta, A. (2008). Asymptotic Theory of Statistics and Probability. Springer.
Feller, W. (1968). An introduction to probability theory and its applications. John Wiley, New York.
Feller, W. (1971). An introduction to probability theory and its applications, vol. II. John Wiley, New York.
Hall, P. (2013). The bootstrap and Edgeworth expansion. Springer Science & Business Media.
Hettmansperger, T.P. and McKean, J.W. (1998). Robutst Nonparanietric. Statistical Methods, London: Arnold.
Kendall, M.G. (1943). Advanced Theory Of Statistics Vol-I. Charles Grin: London.
Lehmann, E.L. (1999). Elements of Large-Sample Theory. Springer, N.Y.
Lo´eve, M. (1977). Graduate Texts in Mathematics, Probability Theory I. Springer-Verlag, New York.
Petrov, Valentin V. (1975). Limit theorems of probability theory: sequences of independent random variables. No.
04; QA273. 67, P4. Oxford, New York.
Pitman, E.J. (1948). Lecture Notes on Nonparametric Statistical Inference: Lectures Given for the University of
North Carolina,[Chapel Hill], 1948. University of North Carolina.
Rao, C.R. (1948). Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation. In Mathematical Proceedings of the Cambridge Philosophical Society (Vol. 44, No. 1,
pp. 50-57). Cambridge University Press.
Sen, P.K. and Singer, M.J. (1993). Large Sample Method in Statistics. Chapman & Hall, New York, United States.
Serfling, R. (1980). Approximation Theorems of Mathematical Statistics. John Wiley, New York.
Shao, J. (2003). Mathematical Statistics, 2nd ed. Springer, New York.
van der Vaart, A. W. (1998). Asymptotic Statistics. Cambridge University Press.
Last Update
16-05-2025
