- Thesis:
- Bachelor in Mathematics
- Author:
- Leonard Späth
- Title:
- Nichtparametrische Dichteschätzung im Additive-Noise-Modell
- Supervisors:
- Sergio Brenner Miguel
- Jan JOHANNES
- Abstract:
- In this thesis we discuss parts of the paper “Hermite Density Deconvolution” by Ousmane B. Sacko from 2019 in detail. We consider the additive noise model in nonparametric statistics. Our aim is to estimate the unknown density of a random variable. The problem is that this random variable is distorted by a noise with a known density. To solve this problem, we combine methods from Hilbert space theory, analysis und statistics. The idea is not to estimate the density itself, but its projection onto a subspace of square-integrable functions. Furthermore, we use the deconvolution method. Using this method we solve the problem of the noise. For our estimator we prove as measure of its quality a formula for the associated mean integrated squared error. We find it is not possible to minimize the bias- and variance-term simultaneously. To deal with this dilemma we discuss an adaptive estimator.
- References:
- O. B. Sacko. Hermite density deconvolution, HAL Id: hal-01978591, 2019.
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |