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 | English |
|---|---|
| Pages (from-to) | 143-192 |
| Number of pages | 50 |
| Journal | Bernoulli |
| Volume | 22 |
| Issue number | 1 |
| DOIs | |
| State | Published - Feb 2016 |
Bibliographical note
Funding Information:This research started when the first author was a Postdoc at EURANDOM, Eindhoven University of Technology, The Netherlands. The research was partly supported by the Deutsche Forschungsgemeinschaft through the FOR 1735 Structural Inference in Statistics. Part of the work on this project was done during a visit of the third author to EURANDOM. We thank three anonymous referees for helpful comments and suggestions.
Keywords
- Adaptive estimation
- Deconvolution
- Distribution function
- Minimax convergence rates
- Plug-in estimator
- Quantile function
- Random fourier multiplier
ASJC Scopus subject areas
- Statistics and Probability