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Language:
The seminar will be in English, if there is at least one non-German speaking participant. Otherwise the presentations will be in German.
Field:
Applied Mathematics, Stochastics
Description of the seminar:
This seminar introduces the asymptotic theory of
nonparametric statistics. A typical problem of nonparametric
statistics is the estimation of a function that is assumed
to lie in a function class. Examples are Hölder classes and
Sobolev balls. The topic of the seminar is the asymptotic
theory of optimal estimation in such settings. We study the
performance of estimators and prove lower bounds for minimax
risks that are available in the model. A main part of the
seminar will be different approaches to obtain such lower
bounds. The seminar follows the book [1]
Possible presentation topics are:
Local polynomial estimation. Projection estimation. (Chapters 1.6, 1.7.1., 1.7.2., two talks)
Lower bounds on the minimax risk based on two hypotheses (Chapters 2.1- 2.5, two talks)
Lower bounds on the minimax risk based on many hypotheses (Chapters 2.6, two talks)
Fano's lemma, Assouad's lemma, van Tree's inequality (Chapter 2.7, two talks)
Pinsker's theorem (Chapters 3.1-3.4, two talks)
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
lecture Probability Theory I or Statistics
I.
Reference:
[1] Alexandre B. Tsybakov Introduction to Nonparametric Statistics, Springer 2009 Link to PDF file
