Deconvolution with supersmooth distributions

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Abstract

Nonparametric deconvolution problems require one to recover an unknown density when the data are contaminated with errors. Optimal global rates of convergence are found under the weighted Lp‐loss (1 ≤ p ≤ ∞). It appears that the optimal rates of convergence are extremely low for supersmooth error distributions. To resolve this difficulty, we examine how high the noise level can be for deconvolution to be feasible, and for the deconvolution estimate to be as good as the ordinary density estimate. It is shown that if the noise level is not too high, nonparametric Gaussian deconvolution can still be practical. Several simulation studies are also presented.

Original languageEnglish (US)
Pages (from-to)155-169
Number of pages15
JournalCanadian Journal of Statistics
Volume20
Issue number2
DOIs
StatePublished - Jun 1992
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Deconvolution
  • Fourier transforms
  • L‐norm
  • global rates of convergence
  • kernel density estimates
  • minimax risks

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