- Article:
- Electronic Journal of Statistics, 15(1), 3551-3573, 2021.
- dx.doi.org/10.1214/21-EJS1870
- 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.
- Preliminary version:
- arXiv:2009.10547
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |
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