Spatial-sign-based high-dimensional white noises test

In this study, we explore the problem of hypothesis testing for white noise in high-dimensional settings, where the dimension of the random vector may exceed the sample sizes. We introduce a test procedure based on spatial-sign for high-dimensional white noise testing. This new spatial-sign-based test statistic is designed to emulate the test statistic proposed by Paindaveine and Verdebout (2016). On high-dimensional sign tests. Bernoulli, 22(3), 1745–1769., but under a more generalized scatter matrix assumption. We establish the asymptotic null distribution and provide the asymptotic relative efficiency of our test in comparison with the test proposed by Feng et al. (2022). Testing for high-dimensional white noise. arXiv:2211.02964. under certain specific alternative hypotheses. Simulation studies further validate the efficiency and robustness of our test, particularly for heavy-tailed distributions.