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Language:
The seminar will be in English, if there is at least one non-German speaking
participant.
Field:
Applied Mathematics, Stochastics
Description of the seminar:
In non-parametric Statistics many proposed estimation strategies are based on a kernel, respectively a projection, approach. These estimators are then dependent on a bandwidth, respectively a dimension parameter. In this seminar, we will consider examples of non-parametric estimators depending on such a smoothing parameter. We will see, that the choice of the parameter is non-trivial. While one can derive an oracle inequality using regularity assumptions on the to-estiamted quantity, those choices are not feasible as they depend on the regularity of the unknown quantity which is again unknown in practice. Our main objective is to introduce so-called data-driven choices of those smoothing parameters and study the risk of the resulting fully data-driven estimators.
The seminar follows the books [1] and [2].
Each participant is expected to give a 60 minutes. A handout containing
the most important definitions and results as well as short sketches of the proofs
should be prepared for the other participants.
Requirements:
The seminar is for advanced Bachelor students and Master students who want to specialize in
statistics and are already familiar with the topics typically covered in the lectures Probability
Theory I and Statistics I.
Reference:
[1] A. B. Tsybakov, Introduction to nonparametric estimation,
Springer Series in Statistics 11, Springer New York, 2009 Link to PDF file
[2] F. Comte,
Nonparametric estimation,
Spartacus-idh, Paris 2017
Online version
