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Last edited on
Apr 18, 2024 by JJ.
Jan JOHANNES Jul 05,2021 Articles

Discussion paper:
arXiv:2107.02120

Title:
Anisotropic spectral cut-off estimation under multiplicative measurement errors

Author:
Sergio Brenner Miguel

Abstract:
We study the non-parametric estimation of an unknown density f with support on R+^d 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 and a regularisation of the inverse of the Mellin transform by a spectral cut-off. The upcoming bias-variance trade-off is dealt with by a data-driven anisotropic choice of the cut-off parameter. In order to discuss the bias term, we consider the 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 spectral cut-off density estimator.
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