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

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.