Univ. Heidelberg
Statistics Group   Institute of Applied Mathematics   Faculty of Mathematics and Computer Science   University Heidelberg
Ruprecht-Karls-Universität Heidelberg Institute of Applied Mathematics Statistics of inverse problems Research Group
german english french



Publications
Cooperations
Research projects
Events
Teaching
Completed theses
People
Contact


Last edited on
Oct 18, 2021 by JJ
.
Discussion paper:
arXiv:2009.10547

Title:
Spectral cut-off regularisation for density estimation under multiplicative measurement errors

Authors:
Sergio Brenner Miguel, Fabienne Comte (Université Paris Descartes) and Jan JOHANNES

Abstract:
We study the non-parametric estimation of an unknown density f with support on R+ based on an i.i.d. sample with multiplicative measurement errors. The proposed fully data driven procedure is based on the estimation of the Mellin transform of the density f, a regularisation of the inverse of the Mellin transform by a spectral cut-off and a data-driven model selection in order to deal with the upcoming bias-variance trade-off. We introduce and discuss further Mellin-Sobolev spaces which characterize the regularity of the unknown density f through the decay of its Mellin transform. Additionally, we show minimax-optimality over Mellin-Sobolev spaces of the data-driven density estimator and hence its adaptivity.

Comment / Contact
Markdown: formatting is possible. All comments are held for moderation.