Topics in nonparametric smoothing

This course studies wavelet based non-parametric smoothing. Topics may include (and are not limited to)

1. Introduction to wavelets: construction, lifting scheme, multiresolution, relation to Fourier analysis and to splines, variance control
2. Locality, sparsity and non-linear smoothing
3. Thresholding, threshold assessment: cross validation, minimax, Stein's Unbiased Risk Estimator, universal threshold, link to extreme value theory
4. Function spaces (Sobolev, Besov)
5. Bayesian smoothing
6. Compressed sensing

Understanding the benefits and limitations of advanced wavelet based nonparametric smoothing, comparing to competitors (splines, Fourier, kernel smoothing and local polynomials)

Literature study and/or classes with focus on one or several aspects (theoretic, computational, application) 

References, bibliography, and recommended reading

M. Jansen. Wavelets from a Statistical Perspective. CRC Press, 2022 (ISBN: 9781032200675)

Course notes

• Université virtuelle

Contacts

Maarten Jansen, see https://maarten.jansen.web.ulb.be/index.html for contact information

Campus

Plaine

Method(s) of evaluation

• written examination

written examination

• Open book examination

• Open question with short answer

Language(s) of evaluation

• english