Abstract: This work is concerned with tests for one-sample mean vectors under high dimensional cases. Existing high dimensional tests for mean vectors base on the assumption of elliptical distribution have been proposed recently. To extend to more distributions, we propose a signed-rank-based test. The proposed test statistic is robust and scalar-invariant. Asymptotic properties of the test statistic are established. Numerical studies show that the proposed test has a good control of the type-I error and is more efficiency. We also employ the proposed method to analyze an ophthalmic data.

Key words: high dimensional analysis, signed-rank, one-sample test, scalar-invariance