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. Asymptotics of the power. Generalization of the Neyman-Pearson lemma. One-sided alternative hypothesis in a monotone likelihood ratio class. Two-sided alternative hypothesis in a one-parameter exponential family. Similarity, Neyman structure. Hypothesis testing in the presence of nuissance parameters. The optimality of classical parametric tests. Asymptotic tests. Generalized likelihood ratio test, derivation of chi-square tests for goodness of fit, homogeneity, and independence. Convergence of the empirical process to a Brownian bridge. Karhunen-Loève expansion of Gaussian processes. Asymptotic analysis of classical non-parametric tests. The relationship between the theory of confidence sets and hypothesis testing.
- Assessment method
- Oral exam
- Bibliography
- lecture notes
- Recommended bibliography
- E. L. Lehmann: Testing Statistical Hypotheses, 2nd Ed., Wiley, New York, 1986. J. Shao: Mathematical Statistics, 2nd Ed., Springer, New York, 2003.