arXiv 3 Jul 2025 · Econometrics
arXiv:2507.02293 · PDF · Extracted main text
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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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 | Gilraine, Gu, and McMillan (2020) A New Method for Estimating Teacher Value-Added | 1.000 | 6 | 5 | 100% |
| 2 | Jiang and Zhang (2009) General Maximum Likelihood Empirical Bayes Estimation of Normal Means | 1.000 | 6 | 3 | 100% |
| 3 | Liu, Moon, and Schorfheide (2020) Forecasting With Dynamic Panel Data Models | 1.000 | 5 | 4 | 100% |
| 4 | Ghosal and van der Vaart (2001) Entropies and Rates of Convergence for Maximum Likelihood and Bayes Estimation for Mixtures of Normal Densities | 0.874 | 8 | 2 | 100% |
| 5 | Chen (2024) Empirical Bayes When Estimation Precision Predicts Parameters | 0.843 | 3 | 3 | 100% |
| 6 | Jiang (2020) On General Maximum Likelihood Empirical Bayes Estimation of Heteroscedastic IID Normal Means | 0.843 | 3 | 3 | 100% |
| 7 | Banerjee, Fu, James, Mukherjee, and Sun (2023) Nonparametric Empirical Bayes Estimation on Heterogeneous Data | 0.811 | 4 | 2 | 100% |
| 8 | Cressie and Borkent (1986) The Moment Generating Function Has Its Moments | 0.737 | 3 | 2 | 100% |
| 9 | Efron (2011) Tweedie's Formula and Selection Bias | 0.737 | 3 | 2 | 100% |
| 10 | Gu and Koenker (2017) Unobserved Heterogeneity in Income Dynamics: An Empirical Bayes Perspective | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 28 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Compound decisions and empirical Bayes via Bayesian nonparametrics | 0.405 | 1 | 1 |