Calibrating the Scan Statistic: Finite Sample Performance Versus Asymptotics
扫描统计量的校准：有限样本表现与渐近理论
Abstract 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 criticised for losing too much power for short signals. We explain this…