Note on Mean Vector Testing for High-Dimensional Dependent Observations

For the mean vector test in high dimension, Ayyala et al.(2017,153:136-155) proposed new test statistics when the observational vectors are M dependent. Under certain conditions, the test statistics for one-same and two-sample cases were shown to be asymptotically normal. While the test statistics and the asymptotic results are valid, some parts of the proof of asymptotic normality need to be corrected. In this work, we provide corrections to the proofs of their main theorems. We also note a few minor discrepancies in calculations in the publication.