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Inference on a distribution from noisy draws

Author

Listed:
  • Koen Jochmans

    (Institute for Fiscal Studies and University of Cambridge)

  • Martin Weidner

    (Institute for Fiscal Studies and University College London)

Abstract
We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other fixed-effect models for panel data. We use an asymptotic embedding where the noise shrinks with the sample size to calculate the leading bias in the empirical distribution arising from the presence of noise. The leading bias in the empirical quantile function is equally obtained. These calculations are new in the literature, where only results on smooth functionals such as the mean and variance have been derived. Given a closed-form expression for the bias, bias-corrected estimator of the distribution function and quantile function can be constructed. We provide both analytical and jackknife corrections that recenter the limit distribution and yield confidence intervals with correct coverage in large samples. These corrections are non-parametric and easy to implement. Our approach can be connected to corrections for selection bias and shrinkage estimation and is to be contrasted with deconvolution. Simulation results confirm the much-improved sampling behavior of the corrected estimators.

Suggested Citation

  • Koen Jochmans & Martin Weidner, 2019. "Inference on a distribution from noisy draws," CeMMAP working papers CWP44/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:44/19
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    References listed on IDEAS

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    Cited by:

    1. Magnac, Thierry & Roux, Sébastien, 2021. "Heterogeneity and wage inequalities over the life cycle," European Economic Review, Elsevier, vol. 134(C).
    2. Okui, Ryo & Yanagi, Takahide, 2019. "Panel data analysis with heterogeneous dynamics," Journal of Econometrics, Elsevier, vol. 212(2), pages 451-475.
    3. Ryo Okui & Takahide Yanagi, 2020. "Kernel estimation for panel data with heterogeneous dynamics," The Econometrics Journal, Royal Economic Society, vol. 23(1), pages 156-175.
    4. St'ephane Bonhomme & Martin Weidner, 2019. "Posterior Average Effects," Papers 1906.06360, arXiv.org, revised Sep 2021.
    5. Laurent Barras & Patrick Gagliardini & Olivier Scaillet, 2022. "Skill, Scale, and Value Creation in the Mutual Fund Industry," Journal of Finance, American Finance Association, vol. 77(1), pages 601-638, February.
    6. Gobillon, Laurent & Magnac, Thierry & Roux, Sébastien, 2022. "Lifecycle Wages and Human Capital Investments: Selection and Missing Data," TSE Working Papers 22-1299, Toulouse School of Economics (TSE).

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    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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