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Keywords:

  • bandwidth;
  • Berkson errors;
  • deconvolution;
  • density estimation;
  • Matlab code for deconvolution estimator;
  • Matlab code for nonparametric regression with errors-in variables;
  • measurement errors;
  • nonparametric curve estimation;
  • R package decon;
  • regression estimation

Summary

Estimating a curve nonparametrically from data measured with error is a difficult problem that has been studied by many authors. Constructing a consistent estimator in this context can sometimes be quite challenging, and in this paper we review some of the tools that have been developed in the literature for kernel-based approaches, founded on the Fourier transform and a more general unbiased score technique. We use those tools to rederive some of the existing nonparametric density and regression estimators for data contaminated by classical or Berkson errors, and discuss how to compute these estimators in practice. We also review some mistakes made by those working in the area, and highlight a number of problems with an existing R package decon.