Estimation of distribution functions in measurement error models

Research output: Contribution to journalArticlepeer-review


Many practical problems are related to the pointwise estimation of distribution functions when data contain measurement errors. Motivation for these problems comes from diverse fields such as astronomy, reliability, quality control, public health and survey data.Recently, Dattner et al. (2011) showed that an estimator based on a direct inversion formula for distribution functions has nice properties when the tail of the characteristic function of the measurement error distribution decays polynomially. In this paper we derive theoretical properties for this estimator for the case where the error distribution is smoother and study its finite sample behavior for different error distributions. Our method is data-driven in the sense that we use only known information, namely, the error distribution and the data. Application of the estimator to estimating hypertension prevalence based on real data is also examined.

Original languageEnglish
Pages (from-to)479-493
Number of pages15
JournalJournal of Statistical Planning and Inference
Issue number3
StatePublished - Mar 2013

Bibliographical note

Funding Information:
The first author was supported by BSF Grant 2006075 . The authors thank Alexander Goldenshluger for helpful discussions.


  • Adaptive estimator
  • Deconvolution
  • Error in variables
  • Prevalence

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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