Statistical Inference
| Title | ΣΤΑΤΙΣΤΙΚΗ ΣΥΜΠΕΡΑΣΜΑΤΟΛΟΓΙΑ / Statistical Inference |
| Code | 0569Α |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Spring |
| Common | Yes |
| Status | Active |
| Course ID | 600019649 |
Programme of Study: UPS of School of Mathematics (2014-today)
Registered students: 25
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Elective Courses belonging to the selected specialization | Spring | - | 5.5 |
| Academic Year | 2020 – 2021 |
| Class Period | Spring |
| Instructors from Other Categories |
|
| Weekly Hours | 4 |
| Class ID | 600166726
|
| Section | Instructors |
|---|---|
| 1. ΕΡΓΑΣΤΗΡΙΟ | Theodora Vlachou |
| 2. ΤΜΗΜΑ Α | Stavros Chatzopoulos |
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/1/600166726
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
Prerequisites
Required Courses
- 0502 Probability Theory I
- 0505 Probability Theory II
- 0534 Mathematical Statistics
General Prerequisites
Probability Theory I and II, Statistics, Mathematical Statistics
Learning Outcomes
Upon successful completion of the course students will:
1. be familiar with the theoretical background of case tests;
2. be able to apply Neymann-Pearson's fundamental lemma to construct hypothesis testing;
3. be able for constructing Uniformly Strong Hypothesis Tests;
4. be familiar with the monotone likelihood ratio property and the generalized likelihood ratio;
5. become familiar with the relationship between confidence intervals and hypothesis tests and with the theoretical background of the hypothesis tests in the general linear model and the analysis of variance.
General Competences
- Apply knowledge in practice
- Make decisions
- Work autonomously
- Work in teams
- Generate new research ideas
- Advance free, creative and causative thinking
Course Content (Syllabus)
Introduction to testing hypothesis - Selecting the test procedure - Testing
simple hypothesis - Neyman-Pearson’s fundamental lemma - Uniformly most powerful
tests - Tests for the parameters of one or two normal populations - Likelihood ratio tests. Tests for the parameters of the general linear model.
Keywords
hypothesis, tests, Neyman-Pearson’s lemma, Likelihood ratio tests
Educational Material Types
- Book
- e-book
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Communication with Students
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 132 | 4.4 | ✓ | ||
| Tutorial | 15 | 0.5 | |||
| Exams | 3 | 0.1 | |||
| Total | 150 | 5 |
Student Assessment
Description
Students are assessed either by two exculpatory written midterms examinations or by a written examination at the end of the semester.
Student Assessment methods
- Written Assignment (Formative, Summative)
- Written Exam with Problem Solving (Formative)
- midterms
Bibliography
Course Bibliography (Eudoxus)
Δαμιανού, Χ. & Κούτρας Μ. (1998). Εισαγωγή στη Στατιστική ΙΙ. Εκδόσεις Συμμετρία, Αθήνα. [45264]
Κολυβά-Μαχαίρα, Φ. (1985). Μαθηματική Στατιστική, Τόμος Ι, Εκτιμητική. Εκδόσεις Ζήτη, Θεσσαλονίκη. [11098]
Κολυβά-Μαχαίρα, Φ. & Χατζόπουλος Στ. Α. (2016). Μαθηματική Στατιστική, Έλεγχοι Υποθέσεων. [ηλεκτρ. βιβλ.] Αθήνα: Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών. Διαθέσιμο στο: http://hdl.handle.net/11419/1899320117. [320117]
Παπαϊωάννου, Τ. & Φερεντίνος, Κ. (2002). Μαθηματική Στατιστική, 2η Έκδοση. Εκδόσεις Σταμούλη, Αθήνα. [22888]
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
22-07-2020
