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arXiv · 1303.1698

Adaptive quantile estimation in deconvolution with unknown error distribution

Itai Dattner·Markus Reiß·Mathias Trabs
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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.

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Itai Dattner, Markus Reiß, Mathias Trabs. 2016-01-15. Adaptive quantile estimation in deconvolution with unknown error distribution. https://doi.org/10.3150/14-bej626

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