Mean vector testing for high-dimensional dependent observations.
J Multivariate Analysis 2017; 153:136-155.
When testing for the mean vector in a high-dimensional setting, it is generally assumed that the observations are independently and identically distributed. However if the data are dependent, the existing test procedures fail to preserve type I error at a given nominal significance level. We propose a new test for the mean vector when the dimension increases linearly with sample size and the data is a realization of an M-dependent stationary process. The order M is also allowed to increase with the sample size. Asymptotic normality of the test statistic is derived by extending the Central Limit Theorem for M-dependent processes using two-dimensional triangular arrays. The cost of ignoring dependence among observations is assessed in finite samples through simulations. J Multivariate Analysis 2017; 153:136-155.
Ayyala, Deepak Nag; Park, Junyong; and Roy, Anindya, "Mean vector testing for high-dimensional dependent observations." (2017). Faculty Research 2017. 20.