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

Autor:	Miguel, Sergio Brenner, Comte, Fabienne, Johannes, Jan
Rok vydání:	2020
Předmět:	Mathematics - Statistics Theory Primary 62G05 secondary 62G07 62C20
Druh dokumentu:	Working Paper
Popis:	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: 22 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2009.10547 Zobrazit plný text záznamu View this record from Arxiv