High dimensional Mean Test for Temporal Dependent Data

TL;DR

This paper introduces a new high-dimensional mean test for temporally dependent data that is computationally efficient, theoretically robust, and applicable without restrictive distributional assumptions.

Contribution

It presents a novel testing method that relaxes common assumptions and offers reduced computational complexity for high-dimensional, temporally dependent data.

Findings

Asymptotic normality established without Gaussian or M-dependence assumptions

Significant computational advantages demonstrated in simulations

Improved performance over existing methods in large-scale scenarios

Abstract

This paper proposes a novel test method for high-dimensional mean testing regard for the temporal dependent data. Comparison to existing methods, we establish the asymptotic normality of the test statistic without relying on restrictive assumptions, such as Gaussian distribution or M-dependence. Importantly, our theoretical framework holds potential for extension to other high-dimensional problems involving temporal dependent data. Additionally, our method offers significantly reduced computational complexity, making it more practical for large-scale applications. Simulation studies further demonstrate the computational advantages and performance improvements of our test.