- Thesis:
- Bachelor in Mathematics
- Author:
- Laura Lecinena Pastor
- Title:
- Rho-Schätzer: eine neue Schätzmehode
- Supervisor:
- Jan JOHANNES
- Abstract:
- In this thesis we consider the problem of creating an universal, optimal and robust estimator. Therefore we define the so called ρ-estimator, for which quadratic risk we calculate an upper bound first for countable and than for uncountable models. This gives us the first step to being able to proof their optimality and robustness. Furthermore, we bound the minimax risk for generall models and more precise for histogramtype models and VC-subgraphs. Finally, we study the connection between the ρ-estimator and the maximum-likelihood estimator, showcasing it exemplarily for histogramtype models.
References:- Y. Baraud, L. Birgé, and M. Sart. A new method for estimation and model selection: Rho-estimation, Inventiones mathematicae, 207(2):425–517, 2016.
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |