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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:
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)
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
