Mean vector testing for high dimensional dependent observations

TL;DR

This paper introduces a new statistical test for the mean vector in high-dimensional, dependent data scenarios, addressing the limitations of existing methods that assume independence.

Contribution

The paper develops a novel test for high-dimensional mean vectors that accounts for dependence in data, allowing the dependence order to grow with sample size.

Findings

The proposed test maintains correct type I error under dependence.

Simulation results show the cost of ignoring dependence leads to inflated error rates.

The test is applicable when data are from an M-dependent stationary process.

Abstract

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 result for M -dependent processes using two dimensional triangular arrays. Finite sample simulation results indicate the cost of ignoring dependence amongst observations.