Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |

2023/05/18 by jj

- Preliminary discussion:
- Wednesday, April 19th, 2021, 11:15, MΛTHEMΛTIKON, INF 205, 4th floor, room 4.414
- Registration:
- Please register for the seminar by using MÜSLI.
**Time and location**of the seminar:- t.b.a
- Contact:
- Bianca Neubert <neubert[at]math.uni-heidelberg.de>
- Jan JOHANNES <johannes[at]math.uni-heidelberg.de>
- Questions, please directly by email or by using the contact form.
- 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:
- Deconvolution problems occur in many fields of
nonparametric statistics, for example, density estimation
based on contaminated data, nonparametric regression with
errors-in-variables, image and signal deblurring. As
applications of deconvolution procedures concern many
real-life problems in econometrics, biometrics, medical
statistics, image reconstruction, one can realize an
increasing number of applied statisticians who are
interested in nonparametric deconvolution methods; on the
other hand, some deep results from Fourier analysis,
functional analysis, and probability theory are required to
understand the construction of deconvolution techniques and
their properties so that deconvolution is also particularly
challenging for mathematicians. In this seminar we will
consider these deconvolution problems following the
book
**[1]**. - Possible presentation topics are:
**Density Deconvolution**- Deconvolution and Kernel estimator (p. 5-13)
- Wavelet based and Ridge estimators (p. 14-23)
- General consistency (p. 23-32)
- Optimal convergence rate: Upper bound for the MSE (p. 32-41)
- Optimal convergence rate: Upper bound for the MISE (p. 41-50)
- Lower bound for the MSE (p. 50-58)
- Lower bound for the MISE (p. 58-63)
- Unknown error densities: Deterministic constrains (p. 78-84)
- Unknown error densities: Additional data & Replicated measurements(p. 84-91)

- 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. Meister*Deconvolution problems in nonparametric statistics*, Lecture Notes in Statistics 193, Springer 2009 Link to PDF file