José Luis Montiel Olea, Ekaterina Zubova
arXiv 6 Jul 2026 · Econometrics
arXiv:2607.05350 · PDF · DOI · OpenAlex · Extracted main text
This paper presents a computational approach to find an approximately minimax estimator for the classical Bounded Normal Mean problem. The suggested procedure is the Bayes estimator corresponding to an approximately least-favorable distribution obtained from a stochastic mirror ascent routine for concave maximization. The paper shows that both the approximately least-favorable distribution and the approximately minimax estimator are indeed close (in a sense we make precise) to their desired targets. Simulation evidence suggests that the approximately minimax estimator can yield, with a reasonable amount of compute, risk improvements from 6% to almost 18% relative to the minimax linear estimator (which is known to admit a maximal improvement of 20%). The approximately minimax estimator is then applied to the problem of how to best aggregate the information contained in local projections and vector autoregressions to estimate an impulse response coefficient.
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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 | Johnstone, I. M (2019) Gaussian Estimation: Sequence and Wavelet Models | 1.000 | 11 | 4 | 100% |
| 2 | Armstrong, T. B., P. Kline, and L. Sun (2025) Adapting to Misspecification | 1.000 | 8 | 3 | 100% |
| 3 | Casella, G. and W. E. Strawderman (1981) Estimating a Bounded Normal Mean | 1.000 | 6 | 4 | 100% |
| 4 | Donoho, D. L., R. C. Liu, and B. MacGibbon (1990) Minimax Risk Over Hyperrectangles, and Implications | 1.000 | 5 | 3 | 100% |
| 5 | Bubeck, S (2015) Convex Optimization: Algorithms and Complexity | 0.928 | 4 | 3 | 100% |
| 6 | Chamberlain, G (2000) Econometric applications of maxmin expected utility | 0.928 | 4 | 3 | 100% |
| 7 | Montiel Olea, J. L., M. Plagborg-Mller, E. Qian, and C. K. Wolf (2026) Double Robustness of Local Projections and Some Unpleasant VARithmetic | 0.874 | 10 | 2 | 100% |
| 8 | Ghosh, M. N (1964) Uniform approximation of minimax point estimates | 0.874 | 5 | 2 | 100% |
| 9 | Ibragimov, I. A. and R. Z. Has'minskii (1985) On nonparametric estimation of the value of a linear functional in Gaussian white noise | 0.874 | 5 | 2 | 100% |
| 10 | Guggenberger, P. and J. Huang (2025) On the numerical approximation of minimax regret rules via fictitious play | 0.843 | 3 | 3 | 100% |
Showing the top 10 of 148 scored citations.