- Thesis:
- Master in Mathematics 50%
- Author:
- Sarah Hoffmann
- Title:
- Testen nichtparametrischer Hypothesen für Dichten
- Supervisors:
- Bianca Neubert
- Jan JOHANNES
- Abstract:
- This thesis focuses on minimax optimal goodness-of-fit testing in a nona- symptotic framework. The aim is to design a statistical test that can evaluate a hypothesis concerning the underlying probability density function f based on given data. The test is constructed using the Fourier coefficients fj of the density function, which also play a crucial role in deriving upper and lower bounds for the minimax separation radius. This radius determines how far an object must be from the null hypothesis for a statistical test to reliably detect the difference. Both Type I and Type II errors are considered in the process. Subsequently, the theoretical findings are supported by simulations, which demonstrate how effectively the test identifies deviations from the uniform distribution on the interval [0, 1) across different probability density functions.
- Reference:
- S. Schluttenhofer. Adaptive Minimax Testing for Inverse Problems, Dissertation, Ruprecht-Karls-Universität Heidelberg, 2020.
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |