Optimal detection of sparse gamma scale admixture with twice the null mean

In a recent paper on sparse gamma scale mixture detection, lower bounds to optimal rates were derived in 4 different local alternative scenarios. Tests were presented attaining these rates in 3 of the scenarios, showing the bounds to be sharp in those cases. In this note we present a test that attains the bound in the fourth scenario, where the contaminating component has twice the null mean, showing the derived bound there to also be sharp. We also present a single test that attains the optimal rate in all 4 scenarios.