SUPERCONSISTENCY OF TESTS IN HIGH DIMENSIONS

Abstract To assess whether there is some signal in a big database, aggregate tests for the global null hypothesis of no effect are routinely applied practice before more specialized analysis carried out. Although plethora available, each test has its strengths but also blind spots. In Gaussian sequence model, we study it possible to obtain with substantially better consistency properties than likelihood ratio (LR; i.e., Euclidean norm-based) test. We establish an impossibility result, showing that high-dimensional framework consider, set alternatives which may improve upon LR (i.e., superconsistency points) always asymptotically negligible relative volume sense.