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Mathematical Statistics (ΣΕΕ1): Διαφορά μεταξύ των αναθεωρήσεων

Mathematical Statistics (ΣΕΕ1): Διαφορά μεταξύ των αναθεωρήσεων

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[[Graduate Courses Outlines]] - [https://math.uoi.gr  Department of Mathematics]
* [[Μαθηματική Στατιστική (ΣEE1)|Ελληνική Έκδοση]]
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=== General ===
=== General ===
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! Course Website (URL)
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| See [https://ecourse.uoi.gr/ eCourse], the Learning Management System maintained by the University of Ioannina.
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=== Attached Bibliography ===
=== Attached Bibliography ===


Books in English
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# Casella, G. and Berger, R.L. (2002). Statistical Inference. Duxbury Press; 2nd edition.
<!-- https://wiki.math.uoi.gr/index.php/%CE%A0%CF%81%CF%8C%CF%84%CF%85%CF%80%CE%BF:MAM126-Biblio -->
# Mood A. et al. (1974). Introduction to the theory of Statistics. McGraw-Hill.
# Roussas G. (1997). A course in Mathematical Statistics. Academic Press.
# Hogg, R and Craig, A. (1978). Introduction to Mathematical Statistics.
# Lehmann, E.L. and Casella, G. (1998). Theory of point estimation. Springer; 2nd edition.
# Bickel, P.J. and Doksum, K.A. (1977). Mathematical Statistics, Basic Ideas and Selected Topics, Vol. 1. Holden-Day.
# Rohatgi, V.K. (1976). An Introduction to Probability Theory and Mathematical Statistics. John Wiley and Sons, New York.
# Rao, C. R. (1973). Linear Statistical Inference and its Applications. Wiley: 2nd edition.
# Lehmann, E.L. and Romano, J.P. (2005). Testing statistical hypotheses. Springer; Third edition, New York.
# Van der Vaart (1998). Asymptotic Statistics. Cambridge University Press.


Books in Greek
{{MAM126-Biblio}}
# Τ. ΠΑΠΑΙΩΑΝΝΟΥ-Κ. ΦΕΡΕΝΤΙΝΟΥ: Μαθηματική Στατιστική Εκδόσεις Σταμούλη.
# Ηλιόπουλος, Γ. (2013). Βασικές Μέθοδοι Εκτίμησης Παραμέτρων. Εκδόσεις Σταμούλη; 2η έκδοση.

Τελευταία αναθεώρηση της 16:38, 15 Ιουνίου 2023

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
  1. Working independently
  2. Decision-making
  3. Production of free, creative and inductive thinking
  4. 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.
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