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| Detailed information |
| Pre-requisites |
(*)keine
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| Original study plan |
Bachelor's programme Statistics 2012W |
| Objectives |
To understand and learn techniques of Mathematical Statistics. To develop the ability of proper application of these methods.
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| Subject |
Properties of sample. Sums of random variables. Sampling from Normal distribution.
Order statistics. Random generator.
Principles of Data Reduction -sufficiency, likelihood, equivariance principle.
Point estimation, estimation. Moment estimator, MLE, Bayes-estimator.
Methods for evaluation of estimators (MSE,Bias)
Best unbiased estimator, (Frechét-)Cramér-Rao inequality.
Fisher-Information. Rao-Blackwell Theorem. Sufficient Statistics. Uniqueness of estimator and Lehmann-Scheffé Theorem. Complete Statistics. Loss functions and Risk. Bayes Risk.
Hypothesis testing.
Methods for Evaluation of
Tests: Likelihood ratio test (LRT). LRT and nuisance parameter. LRT and Sufficiency. Bayes-Tests. Power function. Size of tests. Unbiased Tests. UMP Tests. Neyman-Pearson Lemma.
Karlin-Rubin Theorem. Monotone LRT, stochastic Ordering. p-Values. Fisher Exact Test.
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| Criteria for evaluation |
Exam.
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| Methods |
Lecture.
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| Language |
German |
| Study material |
G. Casella and R.L. Berger, „Statistical Inference“, 2nd edition, Duxbury Advanced Series
Robert Hafner, Wahrscheinlichkeitsrechnung und Statistik, Springer Verlag, 1989
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| Changing subject? |
No |
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