Minimax Risk Nonattainment in Nondominated Settings

Computational evidence that minimax optimal tests may not exist outside dominated settings

0.0020
Max Attainment Gap (ND)
0.5%
Near-Optimal Tests
0.0143
Minimax Risk (n=64)
0.0391
Peak Singularity Gap

Attainment Gap: ND vs Dominated

Convergence with Test Count

Singularity vs Gap

Risk Distribution

Results Summary

nMinimax (ND)Best Test (ND)Gap (ND)Gap (D)
80.02010.02190.00180.0886
160.01550.01610.00050.1118
320.01470.01570.00100.0826
640.01450.01600.00140.0466
1280.01480.01690.00200.0711