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Inference on a distribution from noisy draws

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  • Jochmans, K.
  • Weidner, M.

Abstract

We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of the random variable. This is common practice in many settings, including the evaluation of teacher value-added and the assessment of firm efficiency through stochastic-frontier models. 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. Analytical and jackknife corrections for the empirical distribution are derived that recenter the limit distribution and yield confidence intervals with correct coverage in large samples. A similar adjustment is also presented for the quantile function. 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. An empirical illustration on the estimation of a stochastic-frontier model is also provided.

Suggested Citation

  • Jochmans, K. & Weidner, M., 2019. "Inference on a distribution from noisy draws," Cambridge Working Papers in Economics 1946, Faculty of Economics, University of Cambridge.
  • Handle: RePEc:cam:camdae:1946
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    Cited by:

    1. Okui, Ryo & Yanagi, Takahide, 2019. "Panel data analysis with heterogeneous dynamics," Journal of Econometrics, Elsevier, vol. 212(2), pages 451-475.
    2. Ryo Okui & Takahide Yanagi, 2020. "Kernel estimation for panel data with heterogeneous dynamics [Econometric tools for analyzing market outcomes]," Econometrics Journal, Royal Economic Society, vol. 23(1), pages 156-175.
    3. Magnac, Thierry & Roux, Sébastien, 2021. "Heterogeneity and wage inequalities over the life cycle," European Economic Review, Elsevier, vol. 134(C).
    4. St'ephane Bonhomme & Martin Weidner, 2019. "Posterior Average Effects," Papers 1906.06360, arXiv.org, revised Sep 2021.

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    More about this item

    Keywords

    bias correction; estimation noise; non-parametric inference; regression to the mean; shrinkage;
    All these keywords.

    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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