- Thesis:
- Bachelor in Mathematics 50%
- Author:
- Sarah HOFFMANN
- Title:
- Data-driven density estimation
- Supervisors:
- Jan JOHANNES
- Abstract:
- This thesis deals with a non-parametric density estimation problem. From a data sample of independent and identically distributed random variables with common density we derive the projection density estimator by a non-parametric approach due to dimension reduction. Some considerations are made in order to study its risk and convergence rate. As the proposed estimator requires an optimal choice of the dimension parameter d, which depends on unknown quantities, a data-driven choice of the parameter is necessary. The main concern of this work is to develop an adaptive method resulting in an effective compromise for the choice of d. In this context, we use Talagrand’s inequality to prove a theorem presenting an upper bound for the error in our method. Subsequently, the theoretical results are illustrated in a simulation study. By means of two examples, the attainable accuracy of the estimators with regard to the true density function are evaluated.
- References:
- F. Comte. Nonparametric estimation, Spartacus-idh, 2019.
- A.B. Tsybakov. Introduction to nonparametric estimation, Springer, 2009.
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |