Multiplicative deconvolution estimator based on a ridge approach
arXiv:2108.01523
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 consists of the estimation of the Mellin transform of the density f and a regularisation of the inverse of the Mellin transform by a ridge approach. The upcoming bias-variance trade-off is dealt with by a data-driven choice of the ridge parameter. In order to discuss the bias term, we consider the Mellin-Sobolev spaces which characterise 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 ridge density estimator.
15 pages, 2 figures, 1 table. arXiv admin note: text overlap with arXiv:2107.02120