| Order statistics. Random generator.
Principles of Data Reduction.
Sufficiency, likelihood, equivariance principle.
Point 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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