Note on High‐Dimensional Spatial–Sign Test for One‐Sample Problem

ABSTRACT We revisit the null distribution of the high‐dimensional spatial–sign test under general covariance structures. We show that the standardized statistic may converge to a non‐Gaussian limit, characterized as a mixture of a normal component and a weighted chi‐square component, rather than to the standard normal distribution. To facilitate practical implementation, we propose a multiplier bootstrap procedure for computing critical values and establish its asymptotic validity for both Rademacher and Gaussian multipliers. Numerical experiments demonstrate that the proposed bootstrap tests deliver accurate size control across a wide range of dependence settings and dimension–sample‐size regimes.