Open Access
2021 Spectral cut-off regularisation for density estimation under multiplicative measurement errors
Sergio Brenner Miguel, Fabienne Comte, Jan Johannes
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Electron. J. Statist. 15(1): 3551-3573 (2021). DOI: 10.1214/21-EJS1870


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.


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Sergio Brenner Miguel. Fabienne Comte. Jan Johannes. "Spectral cut-off regularisation for density estimation under multiplicative measurement errors." Electron. J. Statist. 15 (1) 3551 - 3573, 2021.


Received: 1 September 2020; Published: 2021
First available in Project Euclid: 7 July 2021

Digital Object Identifier: 10.1214/21-EJS1870

Primary: 62G05
Secondary: 62C20 , 62G07

Keywords: Adaptation , Density estimation , inverse problem , Mellin transform , Mellin-Sobolev space , minimax theory , Multiplicative measurement errors

Vol.15 • No. 1 • 2021
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