Adaptive quantile estimation in deconvolution with unknown error distribution

I.M. Dattner, M. Reiß, M. Trabs

Research output: Book/ReportReportAcademic

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Abstract

Quantile estimation in deconvolution problems is studied comprehensively. In particular, the more realistic setup of unknown error distributions is covered. Our plug-in method is based on a deconvolution density estimator and is minimax optimal under minimal and natural conditions. This closes an important gap in the literature. Optimal adaptive estimation is obtained by a data-driven bandwidth choice. As a side result we obtain optimal rates for the plug-in estimation of distribution functions with unknown error distributions. The method is applied to a real data example.
Original languageEnglish
Publishers.n.
Number of pages36
Publication statusPublished - 2013

Publication series

NamearXiv.org
Volume1303.1698 [math.ST]

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