Inference on distribution functions under measurement error

Karun Adusumilli, Daisuke Kurisu, Taisuke Otsu, Yoon Jae Whang

Research output: Contribution to journalArticle


This paper is concerned with inference on the cumulative distribution function (cdf) FX in the classical measurement error model X=X+ϵ. We consider the case where the density of the measurement error ϵ is unknown and estimated by repeated measurements, and show validity of a bootstrap approximation for the distribution of the deviation in the sup-norm between the deconvolution cdf estimator and FX . We allow the density of ϵ to be ordinary or super smooth. We also provide several theoretical results on the bootstrap and asymptotic Gumbel approximations of the sup-norm deviation for the case where the density of ϵ is known. Our approximation results are applicable to various contexts, such as confidence bands for FX and its quantiles, and for performing various cdf-based tests such as goodness-of-fit tests for parametric models of X, two sample homogeneity tests, and tests for stochastic dominance. Simulation and real data examples illustrate satisfactory performance of the proposed methods.

Original languageEnglish
JournalJournal of Econometrics
Publication statusAccepted/In press - 2019 Jan 1
Externally publishedYes


  • Confidence band
  • Deconvolution
  • Measurement error
  • Stochastic dominance

ASJC Scopus subject areas

  • Economics and Econometrics

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