Adaptive quantile estimation in deconvolution with unknown error distribution
arXiv:1303.1698 · doi:10.3150/14-BEJ626
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.
Published at http://dx.doi.org/10.3150/14-BEJ626 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)
References in corpus (7)
- On deconvolution with repeated measurements
- Global uniform risk bounds for wavelet deconvolution estimators
- Deconvolution with unknown error distribution
- On deconvolution of distribution functions
- Estimation of distributions, moments and quantiles in deconvolution problems
- Adaptive circular deconvolution by model selection under unknown error distribution
- A uniform central limit theorem and efficiency for deconvolution estimators