General
| School
|
School of Science
|
| Academic Unit
|
Department of Mathematics
|
| Level of Studies
|
Graduate
|
| Course Code
|
ΣΣΕ1
|
| Semester
|
1
|
| Course Title
|
Mathematical Statistics
|
| Independent Teaching Activities
|
Lectures (Weekly Teaching Hours: 3, Credits: 7.5)
|
| Course Type
|
Special Background
|
| Prerequisite Courses
|
-
|
| Language of Instruction and Examinations
|
Greek
|
| Is the Course Offered to Erasmus Students
|
Yes (in English, reading Course)
|
| Course Website (URL)
|
See eCourse, the Learning Management System maintained by the University of Ioannina.
|
Learning Outcomes
| Learning outcomes
|
The course aims to extend the knowledge which the students have obtained during their undergraduate studies on several themes of Mathematical Statistics and to present some special topics of Mathematical Statistics.
|
| General Competences
|
- Working independently
- Decision-making
- Production of free, creative and inductive thinking
- Criticism and self-criticism
All the above will give to the stundetns the opportunity to work in an international multidisciplinary environment.
|
Syllabus
Extensions of the following subjects: Unbiasdness, Sufficient, Minimal Sufficient, Completeness, Consistency, Theorem of: Rao-Blackwell, Lehmann-Scheffé, Basu. Maximum Likelihood Estimators: Properties-Asymptotic Properties. Decision Theory: minimax, Bayes estimators. Modified Likelihood, EM algorithm, Numerical methods of finding estimators. Confidence intervals: pivotal quantity, Asymptotic method etc. Delta Method- Asymptotic statistics.
Teaching and Learning Methods - Evaluation
| Delivery
|
Classroom (face-to-face)
|
| Use of Information and Communications Technology
|
Use of ICT in communication with students
|
| Teaching Methods
|
| Activity
|
Semester Workload
|
| Lectures
|
39
|
| Study and analysis of bibliography
|
78
|
| Preparation of assignments and interactive teaching
|
70.5
|
| Course total
|
187.5
|
|
| Student Performance Evaluation
|
Final written exam in Greek (in case of Erasmus students in English).
|
Attached Bibliography
- B. Andrews and C. Hopper, The Ricci flow in Riemannian Geometry, Springer, 2011.
- T. Colding and W. Minicozzi, A course in minimal surfaces, Graduate Studies in Mathematics, Volume 121, 2011.
- M. Dajczer and R. Tojeiro, Submanifolds theory beyond an introduction, Springer, 2019.
- J. Jost, Riemannian Geometry and Geometric Analysis, 7th edition, Springer, 2017.
- P. Petersen, Riemannian Geometry, 3rd edition, Graduate Texts in Mathematics, 171, Springer, 2016.