Kairat Mynbaev, Carlos Martins-Filho, Chad Brown
arXiv 13 Aug 2026 · Econometrics
arXiv:2608.13152 · PDF · Extracted main text
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 $x<y$ are continuity points; and (iii) the size of a jump at a prespecified discontinuity. We derive non-asymptotic bias and variance bounds, and establish asymptotic unbiasedness and consistency. Unlike previous work, we do not require $F_Y$ to admit a density, have a mixture representation, or satisfy global Sobolev smoothness assumptions. The framework accommodates arbitrary latent distributions, including those with both discrete and continuous components, and distributions with multiple jumps. These results rely on a link between Fourier inversion theorems and the algebraic structure of a class of estimators proposed in Mynbaev, Martins-Filho and Henderson (2022). A simulation study evaluates feasible tuning procedures and, where available, compares the finite-sample performance of the proposed estimators with existing methods.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Mynbaev, K. T. and Martins-Filho, C. and Henderson, D. J (2022) Nonparametric estimation of unrestricted distributions and their jumps self | 0.941 | 12 | 7 | 83% |
| 2 | I. Dattner and B. Reiser (2013) Estimation of distribution functions in measurement error models | 0.935 | 11 | 4 | 82% |
| 3 | Hall, Peter and S. Lahiri (2008) Estimation of distributions, moments and quantiles in deconvolution problems | 0.836 | 12 | 3 | 58% |
| 4 | I. Dattner and A. Goldenshluger and A. Juditsky (2011) On deconvolution of distribution functions | 0.811 | 4 | 2 | 100% |
| 5 | Fan, Jianqing (1991) On the optimal rates of convergence for nonparametric deconvolution problems | 0.644 | 2 | 2 | 100% |
| 6 | Mihee Lee and Peter Hall and Haipeng Shen and J. S. Marron and Jon T… (2013) Deconvolution estimation of mixture distributions with boundaries | 0.644 | 2 | 2 | 100% |
| 7 | Gugushvili, Shota and van Es, Bert and Spreij, Peter (2011) Deconvolution for an atomic distribution: rates of convergence | 0.644 | 2 | 2 | 100% |
| 8 | van Es, Bert and Gugushvili, Shota and Spreij, Peter (2008) Deconvolution for an atomic distribution | 0.644 | 2 | 2 | 100% |
| 9 | Adell, J. A. and Sanguesa, C (2003) Real inversion formulas with rates of convergence | 0.405 | 1 | 1 | 100% |
| 10 | Borovkov, A (2013) Probability Theory | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 15 scored citations.