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Assumption-Lean Shrinkage and Model Averaging for Spatial Parameters

Harvey Barnhard

arXiv 10 Jun 2026 · Econometrics

arXiv:2606.12324 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Economic decisions often depend on many noisy estimates of quantities such as neighborhood effects, school quality, and hospital performance. Shrinkage estimation can improve decisions by pooling information across related units, but geography, adjacency, and shared characteristics each define a different notion of relatedness, and each implies a different way of pooling. We treat the choice of relatedness as part of the estimation problem, using Stein's Unbiased Risk Estimate (SURE) to form a weighted average over a library of flexible shrinkage estimators. This comparison among the candidate estimators treats no prior or latent covariance structure as a correctly specified model for the parameters being estimated. Each candidate is judged by its SURE value. Under smoothness conditions on the estimators, the SURE-weighted average performs nearly as well as the best fixed weighted average of trained candidates, including nonlinear rules whose reported values use the full vector of noisy estimates. In an application to Opportunity Atlas economic mobility data from 20 commuting zones, the best individual spatial specification varies across zones, yet the SURE-weighted average tracks the best in each zone and reduces estimated mean squared error by about 27% relative to the best-performing non-spatial empirical Bayes baseline in our library of estimators.

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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
1Chetty, R., J. N. Friedman, N. Hendren, M. R. Jones, and S. R. Porter (2026) The Opportunity Atlas: Mapping the Childhood Roots of Social Mobility0.84333100%
2Chen, J (2026) Empirical Bayes When Estimation Precision Predicts Parameters0.8229656%
3Bellec, P. C. and C.-H. Zhang (2021) Second Order Stein: SURE for SURE and Other Applications in High-Dimensional Inference0.7374350%
4Ignatiadis, N. and S. Wager (2019) Covariate-Powered Empirical Bayes Estimation0.73732100%
5Chen, J., L. Lei, T. Sudijono, L. Sun, and T. Xie (2025) Compound Selection Decisions: An Almost SURE Approach0.6936433%
Chettyunmatched citation key Chetty0.64441100%
7Oliveira, N. L., J. Lei, and R. J. Tibshirani (2024) Unbiased Risk Estimation in the Normal Means Problem via Coupled Bootstrap Techniques0.6443267%
8Bergman, P., R. Chetty, S. DeLuca, N. Hendren, L. F. Katz, and C. Pa… (2024) Creating Moves to Opportunity: Experimental Evidence on Barriers to Neighborhood Choice0.64422100%
9Fay, R. E. and R. A. Herriot (1979) Estimates of Income for Small Places: An Application of James-Stein Procedures to Census Data0.64422100%
10Kwon, S (2026) Optimal Shrinkage Estimation of Fixed Effects in Linear Panel Data Models0.64422100%

Showing the top 10 of 148 scored citations. 1 of these could not be matched to a bibliography entry, so only the citation key is shown.