Univ. Heidelberg
Statistics Group   Institute of Applied Mathematics   Faculty of Mathematics and Computer Science   University Heidelberg
Ruprecht-Karls-Universität Heidelberg Statistics of inverse problems Research Group Seminar Nonparametric minimax theory (SS 2022)
english



Time and location
Seminar program
Requirements
References
Last edited on
2022/03/15 von jj
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Preliminary discussion:
Tuesday, April 19th, 2022, 14:00, online

Registration:
Please register for the seminar by using MÜSLI to obtain further details by email.

Time and location of the seminar:
The seminar will be held as a Blockseminar on two days at the end of June and beginning of July 2022.

Contact:
Sergio Brenner Miguel <brennermiguel[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. 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:
  1. Local polynomial estimation. Projection estimation. (Chapters 1.6, 1.7.1., 1.7.2., two talks)
  2. Lower bounds on the minimax risk based on two hypotheses (Chapters 2.1- 2.5, two talks)
  3. Lower bounds on the minimax risk based on many hypotheses (Chapters 2.6, two talks)
  4. Fano's lemma, Assouad's lemma, van Tree's inequality (Chapter 2.7, two talks)
  5. 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

Contact
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