# Note on Mean Vector Testing for High-Dimensional Dependent Observations

## TL;DR

This paper revises the proofs of asymptotic normality for mean vector tests in high-dimensional dependent data, correcting previous errors and clarifying the theoretical foundations of the method.

## Contribution

It provides corrected proofs for the asymptotic normality of mean vector tests under dependence, ensuring the validity of the original statistical approach.

## Key findings

- Corrected proofs of asymptotic normality for the test statistics.
- Identification and clarification of minor calculation discrepancies.
- Reinforcement of the validity of high-dimensional mean testing methods.

## Abstract

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.