Courses

The concept of statistical hypothesis and statistical hypothesis testing. Type I error, type II error, test power. Relationship between tests and confidence intervals. Neuman-Pearson Fundamental Lemma. Uniformly powerful tests. Monotonic likelihood ratio property. Uniformly powerful tests in (uniparametric) families of distributions. Applications to normal populations. (Generalized) likelihood ratio tests. z, t, (for one or two normal populations), X2 and F tests. P-value test. X2-goodness-of-fit tests (for categorical data), independence test in correlation matrices. Empirical distribution function and Kolmogorov-Smirnov test for one or two populations. Bayes tests and minimax tests.