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 drift and volatility estimation (WS 2022/23)
english


Time and location
Seminar program
Requirements
References Last edited on
2022/10/04 von jj.
Preliminary discussion:
Tuesday, October 18th, 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 January and beginning of February 2023.

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:
A diffusion process is uniquely defined by its drift and volatility function. In this seminar, we aim to estimate both functions, volatility and drift function, non parametrically. Here, we will develop estimators based on a regression-type projection estimation and develop upper bounds as well data-driven choices of the upcoming smoothing parameters. We will consider a list of frequently-quoted, fundamental works.

Possible presentation topics are:
[1] Penalised nonparametric mean square estimation of the coefficients of diffusion processes, Comte, Genon-Catalot and Rozenholc, 2007
  1. Drift estimation: Non-adaptive case (1 talk)
  2. Drift estimation: Adaptive drift estimator (1 talk)
  3. Diffusion coefficient: Non-adaptive case (1 talk)
  4. Diffusion coefficient: Adaptive diffusion coefficient estimator (1 talk)
[2] Drift estimation on non-compact support for diffusion models, Comte and Genon-Catalot, 2021
  1. Non-adaptive case (1 talk)
  2. Adaptive drift estimator (1 talk)
[3] Nonparametric drift estimation for i.i.d paths of stochastic differential equations, Comte and Genon-Catalot, 2021
  1. Non-adaptive case (1 talk)
  2. Adaptive drift estimator (1 talk)
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] Comte, Genon-Catalot and Rozenholc Penalised nonparametric mean square estimation of the coefficients of diffusion processes, Bernoulli 2007 Link to PDF file
[2] Comte and Genon-Catalot Drift estimation on non-compact support for diffusion, Stochastic Processes and their Applications, 2021 Link to PDF file
[3] Comte and Genon-Catalot Non-parametric drift estimation for i.i.d. paths of stochastic differential equations, Annals of Statistics 2020 Link to PDF file
Contact
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