Course for international guest/part time students
- Faculty
- Faculty of Science
- Organization
- TTK Department of Probability Theory and Statistics
- Code
- stathv1u0um17em
- Title
- Statistical hypothesis testing (l)
- Usual semester
- Spring
- Published semester
- 2026/27/1
- ECTS
- 3
- Language
- hu
- Learning outcomes
- Knowledge: getting familiar with the modern notions of statistical hypothesis testing Ability: to understand and use statistical hypothesis testing in statisitics Attitude: the need to extend the mathematical knowledge, to gain new analytic and applied programming skills Autonomy and Responsibility: based on the gained knowledge in statistical hypothesis testing, the students are able to decide which tools are the most suitable to solve applied problems
- Course content
- Statistical hypotheses, trials, randomized trials. First-order, second-order error, level, extent, power function. Likelihood ratio test, Neyman-Pearson lemma. One-sided counterhypothesis in a monotone likelihood ratio class. Two-sided counterhypothesis in exponential distribution family. Similarity, Neyman structure. Hypothesis testing in the presence of confounding parameters. The optimality of classical parametric tests. Asymptotic trials. Generalized likelihood ratio test, derivation of chi-square tests. Convergence of the empirical process to a Brownian bridge. Karhunen-Loève expansion of Gaussian processes. Asymptotic analysis of classical non-parametric tests. Invariant and Bayesian tests.
- Assessment method
- exam
- Bibliography
- lecture notes
- Recommended bibliography
- E. L. Lehmann: Testing Statistical Hypotheses, 2nd Ed., Wiley, New York, 1986.