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Large-Scale Estimation under Unknown Heteroskedasticity

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  • Sheng Chao Ho

Abstract

This paper studies nonparametric empirical Bayes methods in a heterogeneous parameters framework that features unknown means and variances. We provide extended Tweedie's formulae that express the (infeasible) optimal estimators of heterogeneous parameters, such as unit-specific means or quantiles, in terms of the density of certain sufficient statistics. These are used to propose feasible versions with nearly parametric regret bounds of the order of $(\log n)^\kappa / n$. The estimators are employed in a study of teachers' value-added, where we find that allowing for heterogeneous variances across teachers is crucial for delivery optimal estimates of teacher quality and detecting low-performing teachers.

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  • Sheng Chao Ho, 2025. "Large-Scale Estimation under Unknown Heteroskedasticity," Papers 2507.02293, arXiv.org.
    • Handle: RePEc:arx:papers:2507.02293
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    References listed on IDEAS

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    1. Raj Chetty & John N. Friedman & Jonah E. Rockoff, 2014. "Measuring the Impacts of Teachers II: Teacher Value-Added and Student Outcomes in Adulthood," American Economic Review, American Economic Association, vol. 104(9), pages 2633-2679, September.
    2. Raj Chetty & John N. Friedman & Jonah E. Rockoff, 2014. "Measuring the Impacts of Teachers I: Evaluating Bias in Teacher Value-Added Estimates," American Economic Review, American Economic Association, vol. 104(9), pages 2593-2632, September.
    3. Jiafeng Chen, 2022. "Empirical Bayes When Estimation Precision Predicts Parameters," Papers 2212.14444, arXiv.org, revised Dec 2025.
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