- Thesis:
- Bachelor in Mathematics
- Author:
- Wiktor Pogorzelski
- Title:
- Nonparametric density estimation for distorted data
- Supervisors:
- Sergio Brenner Miguel
- Jan JOHANNES
- Abstract:
- In this thesis, we want to estimate the density f of a real-valued random variable X where the observations are given by Y = X + ε, with ε denoting a random error as a real-valued random variable. We propose an estimator based on the Fourier transform. Afterwards, we give an upper bound of the mean integrated squared error (MISE) and asymptotic rates of convergence for different classes of errors. Then, we prove a lower bound and confirm that the rates of convergence are minimax optimal. Further, we give a novel data-driven choice of the upcoming smoothing parameter and prove an upper bound of its MISE. Finally, we illustrate our results in a simulation study.
References:- C. Duval and J. Kappus. An adaptive procedure for Fourier estimators: illustration to deconvolution and decompounding, Technical report, arXiv:1802.05104, 2018.
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |