Projection-based High-dimensional Sign Test

This article is concerned with the high-dimensional location testing problem. For settings, traditional multivariate-sign-based tests perform poorly or become infeasible since their Type I error rates are far away from nominal levels. Several modifications have been proposed to address this challenging issue and shown well. However, most of modified sign-based abandon all correlation information, results in power loss certain cases. We propose a projection weighted sign test utilize information. Under mild conditions, we derive optimal direction weights which possesses asymptotically locally best under alternatives. Benefiting using sample-splitting idea for estimating direction, able retain type-I pretty well asymptotic distributions, while it can be also highly competitive terms robustness. Its advantage relative existing methods demonstrated numerical simulations real data example.