Methodology for non-parametric deconvolution when the error distribution is unknown
Aurore Delaigle, Peter Hall
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY | WILEY | Published : 2016
In the non-parametric deconvolution problem, to estimate consistently a density or distribution from a sample of data contaminated by additive random noise, it is often assumed that the noise distribution is completely known or that an additional sample of replicated or validation data is available. Methods also have been suggested for estimating the scale of the error distribution, but they require somewhat restrictive smoothness assumptions on the signal distribution, which can be difficult to verify in practice. We take a completely new approach to the problem, not requiring extra data of any type. We argue that data rarely come from a simple regular distribution, and that this can be exp..View full abstract
We thank Ethan Anderes and Jiashun Jin for helpful discussion, and referees and the Associate Editor for their useful suggestions. Delaigle and Hall were supported by the Australian Research Council. Hall also acknowledges support from the National Science Foundation.