We revisit the null distribution of the high-dimensional spatial-sign test of Wang et al. (2015) under mild structural assumptions on the scatter matrix. We show that the standardized test statistic converges to a non-Gaussian limit, characterized as a mixture of a normal component and a weighted chi-square component. To facilitate practical implementation, we propose a wild bootstrap procedure for computing critical values and establish its asymptotic validity. Numerical experiments demonstrate that the proposed bootstrap test delivers accurate size control across a wide range of dependence settings and dimension-sample-size regimes.

翻译：我们在散度矩阵的温和结构假设下，重新审视了Wang等人（2015）提出的高维空间符号检验在原假设下的分布。我们证明了标准化后的检验统计量收敛于一个非高斯极限，该极限被刻画为一个正态分量与一个加权卡方分量的混合。为便于实际应用，我们提出了一种用于计算临界值的Wild Bootstrap方法，并证明了其渐近有效性。数值实验表明，所提出的Bootstrap检验在广泛的相依性设定以及维度-样本量情形下均能提供精确的尺度控制。