107.079 Mathematische Statistik
Diese Lehrveranstaltung ist in allen zugeordneten Curricula Teil der STEOP.
Diese Lehrveranstaltung ist in mindestens einem zugeordneten Curriculum Teil der STEOP.

2023W, VO, 3.0h, 4.5EC
TUWEL

Merkmale

  • Semesterwochenstunden: 3.0
  • ECTS: 4.5
  • Typ: VO Vorlesung
  • Format der Abhaltung: Präsenz

Lernergebnisse

Nach positiver Absolvierung der Lehrveranstaltung sind Studierende in der Lage...

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.

Inhalt der Lehrveranstaltung

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

Methoden

Lectures, in-class questions and discussions

Prüfungsmodus

Schriftlich

Weitere Informationen

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.

Vortragende Personen

Institut

LVA Termine

TagZeitDatumOrtBeschreibung
Mo.09:00 - 11:0009.10.2023 - 22.01.2024Seminarraum 363 Lectures
Mi.16:00 - 18:0011.10.2023 - 17.01.2024Seminarraum 363 Lectures
Mo.09:00 - 11:0004.12.2023EI 6 Eckert HS Lectures
Mo.11:00 - 12:0015.01.2024Seminarraum 127 Lectures
Mathematische Statistik - Einzeltermine
TagDatumZeitOrtBeschreibung
Mo.09.10.202309:00 - 11:00Seminarraum 363 Lectures
Mi.11.10.202316:00 - 18:00Seminarraum 363 Lectures
Mo.23.10.202309:00 - 11:00Seminarraum 363 Lectures
Mo.30.10.202309:00 - 11:00Seminarraum 363 Lectures
Mo.06.11.202309:00 - 11:00Seminarraum 363 Lectures
Mo.13.11.202309:00 - 11:00Seminarraum 363 Lectures
Mo.20.11.202309:00 - 11:00Seminarraum 363 Lectures
Mo.27.11.202309:00 - 11:00Seminarraum 363 Lectures
Mo.04.12.202309:00 - 11:00EI 6 Eckert HS Lectures
Mi.06.12.202316:00 - 18:00Seminarraum 363 Lectures
Mo.11.12.202309:00 - 11:00Seminarraum 363 Lectures
Mo.18.12.202309:00 - 11:00Seminarraum 363 Lectures
Mi.20.12.202316:00 - 18:00Seminarraum 363 Lectures
Mo.08.01.202409:00 - 11:00Seminarraum 363 Lectures
Mo.15.01.202409:00 - 11:00Seminarraum 363 Lectures
Mo.15.01.202411:00 - 12:00Seminarraum 127 Lectures
Mi.17.01.202416:00 - 18:00Seminarraum 363 Lectures
Mo.22.01.202409:00 - 11:00Seminarraum 363 Lectures

Leistungsnachweis

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.

LVA-Anmeldung

Von Bis Abmeldung bis
04.09.2023 08:00 29.02.2024 18:00

Curricula

Literatur

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.

Vorkenntnisse

Probability theory, multivariate calculus and linear algebra

Sprache

Englisch