Gaussian approximation for high dimensional time series: an application to mean testing

We proposed a Gaussian approximation result for high dimensional weakly dependent sequences without presupposing any dependence structure among dimensions. Based on this approximation theory, I will introduce a comprehensive framework for mean testing in scenarios characterized by sparsity. This framework encompasses specialized cases, such as $\ell_{2}$-type and $\ell_{\infty}$-type test statistics.