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

Kairat Mynbaev, Carlos Martins-Filho and Chad Brown

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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

Date: 2026-08
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