Mathematical Statistics
| Title | ΜΑΘΗΜΑΤΙΚΗ ΣΤΑΤΙΣΤΙΚΗ / Mathematical Statistics |
| Code | 0534 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Winter |
| Common | Yes |
| Status | Active |
| Course ID | 40000525 |
Programme of Study: UPS of School of Mathematics (2014-today)
Registered students: 61
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Elective Courses belonging to the selected specialization | Winter | - | 5.5 |
| Academic Year | 2021 – 2022 |
| Class Period | Winter |
| Faculty Instructors |
|
| Weekly Hours | 3 |
| Class ID | 600187031
|
Course Type 2021
General Foundation
Course Type 2016-2020
- Scientific Area
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600187031
- eLearning: https://elearning.auth.gr/course/view.php?id=14202
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
Prerequisites
Required Courses
- 0503 Statistics
General Prerequisites
probability theory I, probability theory II
Learning Outcomes
The aim is to understeand and use statistical methods to solve real problems.
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
- Design and manage projects
- Advance free, creative and causative thinking
Course Content (Syllabus)
An introduction to the Mathematical Statistics.
Families of distributions, Exponential family of distribution family - E.F.D., Sufficient and Complete statistics (Fisher–Neyman factorization theorem and use of E.F.D.), Unbiased Minimum Variance Estimator, Cramér-Rao Inequality, Efficient Estimator, Consistent Estimators, Maximum Likelihood Estimators and Moment Estimators, Confidence intervals, Hypothesis Tests (Neyman-Pearson Lemma).
Keywords
Point Estimation, Interval Estimation, Hypothesis Testing
Educational Material Types
- Notes
- Video lectures
- Book
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Course Teaching
- Use of ICT in Communication with Students
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 65 | 2.2 | ✓ | ||
| Reading Assigment | 84 | 2.8 | ✓ | ✓ | |
| Tutorial | 13 | 0.4 | ✓ | ||
| Exams | 3 | 0.1 | |||
| Total | 165 | 5.5 |
Student Assessment
Student Assessment methods
- written exams (Summative)
Bibliography
Course Bibliography (Eudoxus)
Βιβλίο [45263]: Εισαγωγή στη Στατιστική ΜΕΡΟΣ Ι, Δαμιανού Χ.,Κούτρας Μ.
Βιβλίο [11098]: Κολυβά-Μαχαίρα, Φ. (1985). Μαθηματική Στατιστική, Τόμος Ι, Εκτιμητική. Εκδόσεις Ζήτη, Θεσσαλονίκη
Ηλεκτρονικό βιβλίο [320117]: Κολυβά-Μαχαίρα, Φ. & Χατζόπουλος Στ. Α. (2016). Μαθηματική Στατιστική, Έλεγχοι Υποθέσεων. Αθήνα: Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών. Διαθέσιμο στο: http://hdl.handle.net/11419/1899320117
Βιβλίο [22682832]: Βασικές μέθοδοι εκτίμησης παραμέτρων. Ηλιόπουλος Γιώργος
Βιβλίο [22888]: Παπαϊωάννου, Τ. & Φερεντίνος, Κ. (2002). Μαθηματική Στατιστική, 2η Έκδοση. Εκδόσεις Σταμούλη, Αθήνα
Additional bibliography for study
Bickel, P. J. & Doksum, K. A. (1977). Mathematical Statistics: Basic Ideas and Selected Topics. Holden-Day Inc.
Casella , G. & Berger, J. O. (2001). Statistical Inference, 2nd Edition. Brooks Cole.
Fraser, D. A. (1967). Statistics: An Introduction. John Wiley & Sons Inc.
Graybill, F. A. (1974). Introduction to the Theory of Statistics, 3rd edition. McGraw Hill.
Hogg, R. V. & Tanise, E. A. (1977). Probability and Statistical Inference. Collier-MacMillan International Editions.
Lehmann, E.L. (1975). Nonparametrics: Statistical Methods Based on Ranks. Holden-Day, San Francisco.
Lehmann, E. L. (1983). Theory of Point Estimation. John Wiley and sons, Inc., New York.
Mood, A., Graybill, F. & Boes, D. (1974). Introduction to the Theory of Statistics, 3rd edition. McGraw Hill.
Rao, C. R. (2008). Linear Statistical Inference and its Applications, 2nd edition. Wiley Series on Probability and Statistics.
Rice, J. A.(1994). Mathematical Statistics and Data Analysis, 2nd edition. Duxbury Press.
Roussas, G. (2003). An Introduction to Probability and Statistical Inference. Academic Press. An imprint of Elsevier Science.
Last Update
12-10-2021
