• Bernoulli
  • Volume 22, Number 1 (2016), 143-192.

Adaptive quantile estimation in deconvolution with unknown error distribution

Itai Dattner, Markus Reiß, and Mathias Trabs

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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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Bernoulli, Volume 22, Number 1 (2016), 143-192.

Received: May 2013
Revised: April 2014
First available in Project Euclid: 30 September 2015

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adaptive estimation deconvolution distribution function minimax convergence rates plug-in estimator quantile function random Fourier multiplier


Dattner, Itai; Reiß, Markus; Trabs, Mathias. Adaptive quantile estimation in deconvolution with unknown error distribution. Bernoulli 22 (2016), no. 1, 143--192. doi:10.3150/14-BEJ626.

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