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arXiv · 2009.10547

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

Sergio Brenner Miguel·Fabienne Comte·Jan Johannes
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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.

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Sergio Brenner Miguel, Fabienne Comte, Jan Johannes. 2020-09-22. Spectral cut-off regularisation for density estimation under multiplicative measurement errors. https://arxiv.org/abs/2009.10547

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