- Thesis:
- Bachelor in Mathematics
- Author:
- Emma Dingel
- Title:
- Density estimation for functional data under differential privacy
- Supervisor:
- Jan JOHANNES
- Abstract:
- In this paper, we review statistical models which comply with data privacy. In order to satisfy privacy constraints, the functional data are artificially contaminated by independent Wiener processes. We show that the contaminated data have a Wiener density which uniquely characterises the distribution of the original functional data. Afterwards, we construct a nonparametric estimator of the functional density. Furthermore, we derive an upper bound for its mean integrated squared error, which achieves polynomial convergence rates, and we deduce a lower bound on the minimax convergence rates which is close to the convergence rate attained by our estimator.
- References:
- A. Delaigle and A. Meister. Nonparametric density estimation for intentionally corrupted functional data, arXiv:1912.07879, 2019.
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |