Module MA4940-KP05
Test and estimation theory (TSchThKP05)
Duration
1 Semester
Turnus of offer
each summer semester
Credit points
5
Course of studies, specific fields and terms:
- Master CLS 2023, compulsory, mathematics
- Master CLS 2016, compulsory, mathematics
Classes and lectures:
- Test and estimation theory (exercise, 1 SWS)
- Test and estimation theory (lecture, 2 SWS)
Workload:
- 15 hours exam preparation
- 45 hours in-classroom work
- 60 hours private studies
- 30 hours work on project
Contents of teaching:
- Parametric theory and nonparametric hints about point and interval estimation, and statistical tests
- Properties of estimators: consistency, unbiasedness, sufficiency, efficiency
- Construction of estimators: score function, maximum likelihood, bias correction, theorems of Rao-Crámer, Rao-Blackwell, and Lehmann-Schefé, multi-parametric exponential family
- Properties of confidence intervals: exact, coverage probability, pivot statistics
- Construction of Wald, score, and ML confidence intervalls; delta method
- Properties of statistical tests: power function, unbiasedness, best tests, Lemma of Neyman and Pearson, consistency and asymptotic relative efficiency
- Construction of likelihood ratio, Wald, score, MLR, and conditional tests
Qualification-goals/Competencies:
- Students know the definitions of central theoretical concepts in the theory of estimation and testing.
- They have understood properties and construction principles.
- They apply construction principles to problems with one or more parameters.
- They prove properties of estimators and tests.
- They assess tests and estimators by their properties.
- They construe statistical tests and confidence intervals for problems with distributions they did not know before.
Grading through:
- written exam
Responsible for this module:
Literature:
- Lehmann, E.L., Romano, Joseph P. : Testing Statistical Hypotheses ISBN-13 9780387988641
- Lehmann, E.L., Casella, George : Theory of Point Estimation ISBN-13 9780387985022
- Held, L. : Methoden der statistischen Inferenz Spektrum 2008 - ISBN 978-3-8274-1939-2
- Rüger, B. : Test- und Schätztheorie: Band I: Grundlagen Oldenbourg 1999 - ISBN 3 486-23650-4
- Rüger, B. : Test- und Schätztheorie: Band II: Statistische Tests Oldenbourg 2002 - ISBN 3 486-25130-9
Language:
- offered only in German
Notes:
Admission requirements for taking the module:- None (The competencies of the modules listed under 'Requires' are needed for this module, but are not a formal prerequisite)
Admission requirements for participation in module examination(s):
- Examination prerequisites can be defined at the beginning of the semester. If preliminary work is defined, it must have been completed and positively evaluated before the first examination.
Module exam(s):
- MA4940-L1: Test and estimation theory, written exam, 90 min, 100 % of module grade
Last Updated:
22.02.2022