arXiv 8 May 2026 · Econometrics
arXiv:2605.08551 · PDF · DOI · OpenAlex · Extracted main text
Empirical Bayes methods can improve inference on unobservable individual effects by borrowing strength across units. This paper proposes nonparametric empirical Bayes confidence intervals (NP-EBCIs) for unobservable individual effects in a normal means model. The oracle intervals are constructed from posterior quantiles under a point-identified, fully nonparametric prior; feasible intervals replace these quantiles with nonparametric estimates. The NP-EBCIs are asymptotically exact in the sense that both their conditional and marginal coverage probabilities converge to the nominal level. The flexibility of this nonparametric construction has an unavoidable statistical cost. We demonstrate that posterior quantiles, unlike posterior means, inherit the severe ill-posedness of nonparametric deconvolution: the minimax optimal estimation rate is logarithmic. This logarithmic rate is minimax optimal for errors in the conditional coverage probability, and the resulting errors in the marginal coverage probability also vanish at the same logarithmic rate. Despite these slow asymptotic rates, simulations show that the NP-EBCIs remain close to nominal coverage when the prior is non-Gaussian, and deliver substantial length reductions relative to intervals that treat each unit in isolation.
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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 | Morris, Carl N (1983) Parametric empirical Bayes inference: theory and applications | 1.000 | 12 | 3 | 100% |
| 2 | Armstrong, Timothy B and Kolesár, Michal and Plagborg-Møller, Mikkel (2022) Robust empirical bayes confidence intervals | 1.000 | 9 | 4 | 100% |
| 3 | Schennach, Susanne M (2020) Mismeasured and unobserved variables | 1.000 | 6 | 4 | 100% |
| 4 | Walters, Christopher (2024) Empirical Bayes methods in labor economics | 1.000 | 5 | 3 | 100% |
| 5 | Cox, David R (1975) Prediction intervals and empirical Bayes confidence intervals | 0.874 | 5 | 2 | 100% |
| 6 | Zhang, Cun-Hui (2009) Generalized maximum likelihood estimation of normal mixture densities | 0.843 | 4 | 3 | 75% |
| 7 | Zhang, Cun-Hui (1997) Empirical Bayes and compound estimation of normal means | 0.843 | 5 | 3 | 60% |
| 8 | Carroll, Raymond J and Hall, Peter (1988) Optimal rates of convergence for deconvolving a density | 0.737 | 3 | 2 | 100% |
| 9 | Jiang, Wenhua and Zhang, Cun-Hui (2009) General maximum likelihood empirical Bayes estimation of normal means | 0.737 | 3 | 2 | 100% |
| 10 | Berger, James O (1985) Statistical Decision Theory and Bayesian Analysis | 0.644 | 4 | 1 | 100% |
Showing the top 10 of 108 scored citations.