Open Access
February 2016 Adaptive quantile estimation in deconvolution with unknown error distribution
Itai Dattner, Markus Reiß, Mathias Trabs
Bernoulli 22(1): 143-192 (February 2016). DOI: 10.3150/14-BEJ626


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. "Adaptive quantile estimation in deconvolution with unknown error distribution." Bernoulli 22 (1) 143 - 192, February 2016.


Received: 1 May 2013; Revised: 1 April 2014; Published: February 2016
First available in Project Euclid: 30 September 2015

zbMATH: 06543266
MathSciNet: MR3449779
Digital Object Identifier: 10.3150/14-BEJ626

Keywords: adaptive estimation , Deconvolution , distribution function , Minimax convergence rates , Plug-in estimator , quantile function , random Fourier multiplier

Rights: Copyright © 2016 Bernoulli Society for Mathematical Statistics and Probability

Vol.22 • No. 1 • February 2016
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