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 language | English |
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| Publisher | s.n. |
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| Number of pages | 36 |
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| Publication status | Published - 2013 |
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| Name | arXiv.org |
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| Volume | 1303.1698 [math.ST] |
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