Statistical Inference

Course Information
Cycle / Level1st / Undergraduate
Teaching PeriodSpring
Course ID600019649

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

Registered students: 25
OrientationAttendance TypeSemesterYearECTS
CoreElective Courses belonging to the selected specializationSpring-5.5

Class Information
Academic Year2020 – 2021
Class PeriodSpring
Instructors from Other Categories
Weekly Hours4
Class ID
1. ΕΡΓΑΣΤΗΡΙΟTheodora Vlachou
2. ΤΜΗΜΑ ΑStavros Chatzopoulos
Type of the Course
  • Scientific Area
Course Category
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
  • 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.
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
Student Assessment
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
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: [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.
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