EconBase
← All papers

Approximate Minimax Estimation of a Bounded Normal Mean via Stochastic Mirror Ascent

José Luis Montiel Olea, Ekaterina Zubova

arXiv 6 Jul 2026 · Econometrics

arXiv:2607.05350 · PDF · DOI · OpenAlex · Extracted main text

Abstract

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.

Citation extraction

61
references
237
in-text mentions
148
distinct cited
0
self-citations
22,139
main-text words

appendix boundary found by none_found · 100% 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
1Johnstone, I. M (2019) Gaussian Estimation: Sequence and Wavelet Models1.000114100%
2Armstrong, T. B., P. Kline, and L. Sun (2025) Adapting to Misspecification1.00083100%
3Casella, G. and W. E. Strawderman (1981) Estimating a Bounded Normal Mean1.00064100%
4Donoho, D. L., R. C. Liu, and B. MacGibbon (1990) Minimax Risk Over Hyperrectangles, and Implications1.00053100%
5Bubeck, S (2015) Convex Optimization: Algorithms and Complexity0.92843100%
6Chamberlain, G (2000) Econometric applications of maxmin expected utility0.92843100%
7Montiel Olea, J. L., M. Plagborg-Mller, E. Qian, and C. K. Wolf (2026) Double Robustness of Local Projections and Some Unpleasant VARithmetic0.874102100%
8Ghosh, M. N (1964) Uniform approximation of minimax point estimates0.87452100%
9Ibragimov, I. A. and R. Z. Has'minskii (1985) On nonparametric estimation of the value of a linear functional in Gaussian white noise0.87452100%
10Guggenberger, P. and J. Huang (2025) On the numerical approximation of minimax regret rules via fictitious play0.84333100%

Showing the top 10 of 148 scored citations.