- Thesis:
- Master in Mathematics
- Author:
- Felix Schürzinger
- Title:
- Ridge estimators for the drift function of a SDE
- Supervisors:
- Fabienne Comte (Université Paris Cité)
- Jan JOHANNES
- Abstract:
- In this thesis, we explore the application of methods of nonparametric estimation to approximate an unknown regression function given i.i.d. design variables distributed according to an unknown density, as well as tackling the challenge of drift estimation for a one-dimensional, time-homogeneous stochastic differential equation. Specifically, next to a discussion of the necessary assumptions, we construct and compare consistent ridge and least-square projection estimators for these scenarios under different choices of basis. This includes a study of upper- and lower bounds, allowing us to derive optimal rates of convergence, and adaptive estimation procedures that perform an automatic bias-variance tradeoff and achieve the optimal rate. Finally, the practical performance of the estimators is assessed through simulation experiments to illustrate their behavior.
- Reference:
- F. Comte und V. Genon-Catalot. Drift estimation on non compact support for diffusion models, Stochastic Processes and their Applications, 134:174–207, 2021.
- C. Denis, C. Dion-Blanc, und M. Martinez. A ridge estimator of the drift from discrete repeated observations of the solution of a stochastic differential equation, Bernoulli, 27(4), 2021.
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |