107.079 Mathematical Statistics
This course is in all assigned curricula part of the STEOP.
This course is in at least 1 assigned curriculum part of the STEOP.

2023W, VO, 3.0h, 4.5EC
TUWEL

Properties

  • Semester hours: 3.0
  • Credits: 4.5
  • Type: VO Lecture
  • Format: Presence

Learning outcomes

After successful completion of the course, students are able to understand the mathematical foundations of statistical inference, work with basic statistical models and tests, analyse their features and assess their performance. They are also able to apply their theoretical knowledge in a variety of applications.

Subject of course

Foundations

  • Data, models, parameters, statistics
  • Exponential families
  • Sufficient statistics
  • Complete statistics
  • Bayesian models

Estimation

  • Plug-in and moment estimators
  • Maximum likelihood estimators
  • Expectation-maximisation algorithm

Performance

  • Decision theoretic framework
  • Bayes procedures
  • Minimax procedures
  • Unbiased estimation

Asymptotics

  • Consistent estimators
  • In-law approximations
  • Asymptotic efficiency

Testing

  • Statistical hypothesis testing
  • Uniformly most powerful tests
  • Bayes tests
  • Confidence regions

Teaching methods

Lectures, in-class questions and discussions

Mode of examination

Written

Additional information

The schedule of the course is provisional and will be agreed with the students in the first week. If the provisional schedule does not work for you, please drop an email to the lecturer before the start of the semester and indicate your preference.

Lecturers

Institute

Course dates

DayTimeDateLocationDescription
Mon09:00 - 11:0009.10.2023 - 22.01.2024Seminarraum 363 Lectures
Wed16:00 - 18:0011.10.2023 - 17.01.2024Seminarraum 363 Lectures
Mon09:00 - 11:0004.12.2023EI 6 Eckert HS Lectures
Mon11:00 - 12:0015.01.2024Seminarraum 127 Lectures
Mathematical Statistics - Single appointments
DayDateTimeLocationDescription
Mon09.10.202309:00 - 11:00Seminarraum 363 Lectures
Wed11.10.202316:00 - 18:00Seminarraum 363 Lectures
Mon23.10.202309:00 - 11:00Seminarraum 363 Lectures
Mon30.10.202309:00 - 11:00Seminarraum 363 Lectures
Mon06.11.202309:00 - 11:00Seminarraum 363 Lectures
Mon13.11.202309:00 - 11:00Seminarraum 363 Lectures
Mon20.11.202309:00 - 11:00Seminarraum 363 Lectures
Mon27.11.202309:00 - 11:00Seminarraum 363 Lectures
Mon04.12.202309:00 - 11:00EI 6 Eckert HS Lectures
Wed06.12.202316:00 - 18:00Seminarraum 363 Lectures
Mon11.12.202309:00 - 11:00Seminarraum 363 Lectures
Mon18.12.202309:00 - 11:00Seminarraum 363 Lectures
Wed20.12.202316:00 - 18:00Seminarraum 363 Lectures
Mon08.01.202409:00 - 11:00Seminarraum 363 Lectures
Mon15.01.202409:00 - 11:00Seminarraum 363 Lectures
Mon15.01.202411:00 - 12:00Seminarraum 127 Lectures
Wed17.01.202416:00 - 18:00Seminarraum 363 Lectures
Mon22.01.202409:00 - 11:00Seminarraum 363 Lectures

Examination modalities

Written exam. Additional points may be awarded for class participation.

The first exam will take place at the end of the winter semester, on a date to be agreed with attending students. If you wish to take the exam in a subsequent date, please get in touch directly with the lecturer and another exam will be scheduled.

Course registration

Begin End Deregistration end
04.09.2023 08:00 29.02.2024 18:00

Curricula

Literature

Bickel, P.J., & Doksum, K.A. (2015). Mathematical Statistics: Basic Ideas and Selected Topics, Second Edition. Chapman and Hall/CRC.

Shao, J. (2003). Mathematical Statistics, Second Edition. Springer-Verlag.

Previous knowledge

Probability theory, multivariate calculus and linear algebra

Language

English