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 language | American English |
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Pages (from-to) | 143-192 |
Number of pages | 50 |
Journal | Bernoulli |
Volume | 22 |
Issue number | 1 |
DOIs | |
State | Published - Feb 2016 |
Keywords
- Adaptive estimation
- Deconvolution
- Distribution function
- Minimax convergence rates
- Plug-in estimator
- Quantile function
- Random fourier multiplier
All Science Journal Classification (ASJC) codes
- Statistics and Probability