- Thesis:
- Master in Mathematics
- Author:
- Clemens Hecht
- Title:
- Adaptive kernel estimation for i.i.d. Gaussian continuous moving average models
- Supervisors:
- Sergio Brenner Miguel
- Jan JOHANNES
- Abstract:
- In this thesis we study the nonparametric estimation of the square of a kernel function of a continuous moving average process, shortly CMA, where the kernel function is deterministic and square integrable. The estimation is based on i.i.d. observations of the process on a finite time interval. Based on them, we propose projection estimators under various assumptions and provide nonasymptotic upper bounds of their risk, which lead to different rates of convergence, depending on the set of assumptions and regularity conditions. We further provide data-driven estimators in order to solve the bias-variance trade-off and to compensate the unknownness of parameters appearing in the rates we obtain. Lastly, a simulation study shows that the adaptive estimators are working well in practice.
- Reference:
- F. Comte and V. Genon-Catalot. Nonparametric estimation for i.i.d. gaussian continuous time moving average models, Statistical Inference for Stochastic Processes, (24):149-177, 2020.
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |