Bernoulli

  • 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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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.bj/1443620846

Digital Object Identifier
doi:10.3150/14-BEJ626

Mathematical Reviews number (MathSciNet)
MR3449779

Zentralblatt MATH identifier
06543266

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

Citation

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. https://projecteuclid.org/euclid.bj/1443620846


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