Calibrating the scan statistic: finite sample performance vs. asymptotics

Understand

We consider the problem of detecting an elevated mean on an interval with unknown location and length in the univariate Gaussian sequence model.

• Recent results have shown that using scale-dependent critical values for the scan statistic allows to attain asymptotically optimal detection simultaneously for all signal lengths, thereby improving on the traditional scan, but this procedure has been criticized for losing too much power for short signals.
• We explain this discrepancy by showing that these asymptotic optimality results will necessarily be too imprecise to discern the performance of scan statistics in a practically relevant way, even in a large sample context.
• Instead, we propose to assess the performance with a new finite sample criterion.