Mathematical Statistics

Course Information
TitleΜΑΘΗΜΑΤΙΚΗ ΣΤΑΤΙΣΤΙΚΗ / Mathematical Statistics
Cycle / Level1st / Undergraduate
Teaching PeriodWinter
Course ID40000525

Programme of Study: UPS of School of Mathematics (2014-today)

Registered students: 95
OrientationAttendance TypeSemesterYearECTS
CoreElective Courses belonging to the selected specializationWinter-5.5

Class Information
Academic Year2019 – 2020
Class PeriodWinter
Faculty Instructors
Weekly Hours3
Class ID
Course Type 2016-2020
  • Scientific Area
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
  • Face to face
Digital Course Content
The course is also offered to exchange programme students.
Language of Instruction
  • Greek (Instruction, Examination)
Required Courses
  • 0205 Calculus IV
  • 0502 Probability Theory I
  • 0503 Statistics
  • 0505 Probability Theory II
General Prerequisites
Probability theory, calculus
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
  • Advance free, creative and causative thinking
Course Content (Syllabus)
Distributions of functions , of random variables - The exponential family - Sufficiency of a statistic for a parameter or for functions of parameters. The Rao-Blackwel theorem - Completeness and uniqueness - Unbiased estimators with minimum variance - The Cramer-Rao inequality - Efficient statistics - Consistent statistics - Maximum likelihood and moment estimators and their properties - Prior and posterior distributions and Bayes estimators - The minimax principle - Interval estimation. General methods for construction of confidence intervals - Approximate confidence intervals - Confidence regions.
Point estimation, Interval estimation, Maximum likelihood, Unbiased estimators with minimum variance, Bayes
Educational Material Types
  • Notes
  • Book
Use of Information and Communication Technologies
Use of ICT
  • Use of ICT in Communication with Students
Course Organization
Student Assessment
Student Assessment methods
  • Written Exam with Short Answer Questions (Formative, Summative)
  • Written Exam with Problem Solving (Formative, Summative)
Course Bibliography (Eudoxus)
- Μαθηματική Στατιστική-Εκτιμητική της Φ. Κολυβά-Μαχαίρα. - Εισαγωγή στη Στατιστική, Μέρος 2o των Χ. Δαμιανού, Μ. Κούτρα.
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.
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