EconBase
← All papers

Large-Scale Estimation under Unknown Heteroskedasticity

Sheng Chao Ho

arXiv 3 Jul 2025 · Econometrics

arXiv:2507.02293 · PDF · Extracted main text

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.

Citation extraction

28
references
68
in-text mentions
28
distinct cited
0
self-citations
27,891
main-text words

appendix boundary found by appendix_titled_section at “Supplementary Simulation Results” · 99% of the source is main text. Read the extracted text to check this.

Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Gilraine, Gu, and McMillan (2020) A New Method for Estimating Teacher Value-Added1.00065100%
2Jiang and Zhang (2009) General Maximum Likelihood Empirical Bayes Estimation of Normal Means1.00063100%
3Liu, Moon, and Schorfheide (2020) Forecasting With Dynamic Panel Data Models1.00054100%
4Ghosal and van der Vaart (2001) Entropies and Rates of Convergence for Maximum Likelihood and Bayes Estimation for Mixtures of Normal Densities0.87482100%
5Chen (2024) Empirical Bayes When Estimation Precision Predicts Parameters0.84333100%
6Jiang (2020) On General Maximum Likelihood Empirical Bayes Estimation of Heteroscedastic IID Normal Means0.84333100%
7Banerjee, Fu, James, Mukherjee, and Sun (2023) Nonparametric Empirical Bayes Estimation on Heterogeneous Data0.81142100%
8Cressie and Borkent (1986) The Moment Generating Function Has Its Moments0.73732100%
9Efron (2011) Tweedie's Formula and Selection Bias0.73732100%
10Gu and Koenker (2017) Unobserved Heterogeneity in Income Dynamics: An Empirical Bayes Perspective0.73732100%

Showing the top 10 of 28 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Compound decisions and empirical Bayes via Bayesian nonparametrics0.40511