  This article concerns tests for location parameters in cases where the data
dimension is larger than the sample size. We propose a family of tests based on
the optimality arguments in Le Cam (1986) under elliptical symmetric. The
asymptotic normality of these tests are established. By maximizing the
asymptotic power function, we propose an uniformly optimal test for all
elliptical symmetric distributions. The optimality is also confirmed by a Monte
Carlo investigation.
