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

2026-07-06

AI Summary

This study addresses the minimax estimation problem under a bounded normal mean model. The authors propose a novel approach based on the stochastic mirror ascent algorithm to approximate the least favorable prior distribution by solving a concave maximization problem, and then adopt its Bayes estimator as an approximate minimax estimator. This work is the first to introduce stochastic mirror ascent into this class of estimation problems and provides theoretical guarantees for the approximation accuracy. Numerical experiments demonstrate that the proposed estimator reduces risk by 6% to nearly 18% compared to the classical minimax linear estimator. Furthermore, the method is successfully applied to impulse response coefficient estimation, confirming its practical effectiveness.

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.

Problem

• Bounded Normal Mean
• Minimax Estimation
• Impulse Response Estimation
• Least-Favorable Distribution
• Risk Improvement

Innovation

• minimax estimation
• bounded normal mean
• stochastic mirror ascent
• least-favorable prior
• Bayes estimator