Density deconvolution under general assumptions on the distribution of measurement errors

Denis Belomestny, Alexander Goldenshluger

Research output: Contribution to journalArticlepeer-review


In this paper, we study the problem of density deconvolution under general assumptions on the measurement error distribution. Typically, deconvolution estimators are constructed using Fourier transform techniques, and it is assumed that the characteristic function of the measurement errors does not have zeros on the real line. This assumption is rather strong and is not fulfilled in many cases of interest. In this paper, we develop a methodology for constructing optimal density deconvolution estimators in the general setting that covers vanishing and nonvanishing characteristic functions of the measurement errors. We derive upper bounds on the risk of the proposed estimators and provide sufficient conditions under which zeros of the corresponding characteristic function have no effect on estimation accuracy. Moreover, we show that the derived conditions are also necessary in some specific problem instances.

Original languageEnglish
Pages (from-to)615-649
Number of pages35
JournalAnnals of Statistics
Issue number2
StatePublished - 2021

Bibliographical note

Publisher Copyright:
© Institute of Mathematical Statistics, 2021


  • Characteristic function
  • Density deconvolution
  • Density estimation
  • Laplace transform
  • Lower bounds
  • Minimax risk

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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