In this study, we explore a robust testing procedure for the high-dimensional location parameters testing problem. Initially, we introduce a spatial-sign based max-type test statistic, which exhibits excellent performance for sparse alternatives. Subsequently, we demonstrate the asymptotic independence between this max-type test statistic and the spatial-sign based sum-type test statistic (Feng and Sun, 2016). Building on this, we propose a spatial-sign based max-sum type testing procedure, which shows remarkable performance under varying signal sparsity. Our simulation studies underscore the superior performance of the procedures we propose.

翻译：本研究探讨了高维位置参数检验问题的一种稳健检验方法。首先，我们提出了一种基于空间符号的最大型检验统计量，该统计量在稀疏备择假设下表现出优异的性能。随后，我们证明了该最大型检验统计量与基于空间符号的和型检验统计量（Feng and Sun, 2016）之间的渐近独立性。在此基础上，我们提出了一种基于空间符号的最大-和型检验方法，该方法在不同信号稀疏度下均展现出卓越的性能。我们的模拟研究进一步证实了所提方法的优越性。