Mathematical Statistics (ΣΕΕ1)

Graduate Courses Outlines - Department of Mathematics

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

Books in English

1. Casella, G. and Berger, R.L. (2002). Statistical Inference. Duxbury Press; 2nd edition.
2. Mood A. et al. (1974). Introduction to the theory of Statistics. McGraw-Hill.
3. Roussas G. (1997). A course in Mathematical Statistics. Academic Press.
4. Hogg, R and Craig, A. (1978). Introduction to Mathematical Statistics.
5. Lehmann, E.L. and Casella, G. (1998). Theory of point estimation. Springer; 2nd edition.
6. Bickel, P.J. and Doksum, K.A. (1977). Mathematical Statistics, Basic Ideas and Selected Topics, Vol. 1. Holden-Day.
7. Rohatgi, V.K. (1976). An Introduction to Probability Theory and Mathematical Statistics. John Wiley and Sons, New York.
8. Rao, C. R. (1973). Linear Statistical Inference and its Applications. Wiley: 2nd edition.
9. Lehmann, E.L. and Romano, J.P. (2005). Testing statistical hypotheses. Springer; Third edition, New York.
10. Van der Vaart (1998). Asymptotic Statistics. Cambridge University Press.

Books in Greek

1. Τ. ΠΑΠΑΙΩΑΝΝΟΥ-Κ. ΦΕΡΕΝΤΙΝΟΥ: Μαθηματική Στατιστική Εκδόσεις Σταμούλη.
2. Ηλιόπουλος, Γ. (2013). Βασικές Μέθοδοι Εκτίμησης Παραμέτρων. Εκδόσεις Σταμούλη; 2η έκδοση.