Adaptive quantile estimation in deconvolution with unknown error distribution

Itai Dattner, Markus Reiß, Mathias Trabs

Research output: Contribution to journalArticlepeer-review

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 languageAmerican English
Pages (from-to)143-192
Number of pages50
JournalBernoulli
Volume22
Issue number1
DOIs
StatePublished - Feb 2016

Keywords

  • Adaptive estimation
  • Deconvolution
  • Distribution function
  • Minimax convergence rates
  • Plug-in estimator
  • Quantile function
  • Random fourier multiplier

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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