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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
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