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Estimation of distribution functions, their jumps and interval probabilities under measurement error

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  • Kairat Mynbaev
  • Carlos Martins-Filho
  • Chad Brown

Abstract

We consider the classical additive measurement-error model $X=Y+Z$, where the latent random variable $Y$ has unknown distribution $F_Y$ and the error $Z$ has a known distribution. We develop direct estimators for three functionals of $F_Y$: (i) $F_Y(x)$ at continuity points; (ii) interval probabilities $F_Y(y)-F_Y(x)$ when $x

Suggested Citation

  • Kairat Mynbaev & Carlos Martins-Filho & Chad Brown, 2026. "Estimation of distribution functions, their jumps and interval probabilities under measurement error," Papers 2608.13152, arXiv.org.
    • Handle: RePEc:arx:papers:2608.13152
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    File URL: https://arxiv.org/pdf/2608.13152
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    References listed on IDEAS

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    1. Shota Gugushvili & Bert van Es & Peter Spreij, 2011. "Deconvolution for an atomic distribution: rates of convergence," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 1003-1029.
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