Statistics I 1000-135ST1

1. The notion of a statistical model, sample characteristics, the basic theorem of mathematical statistics.
2. Sufficient statistics, minimal sufficient statistics, complete statistics.
3. Estimation of distribution parameters: selected methods of estimation (maximal likelihood estimators, least squares method), properties of estimators (consistency, asymptotic normality, non-biased tests); comparison of estimators for the risk function corresponding to the quadratic loss function; non-biased estimators with minimal variance, information inequality.
4. Verification of statistical hypotheses: the notion of statistical test, error of 1st and 2nd kind, test power, Neyman-Pearson lemma, uniformly strongest tests for families with monotone confidence quotient, tests based on confidence quotient, hypothesis testing in normal models, non-parametric tests (Kolmogorov test and Wilcoxon test), chi-square test.
5. Confidence intervals