High dimensional Mean Test for Temporal Dependent Data

2025-11-27

AI Summary

This paper addresses the mean testing problem for high-dimensional time-dependent data without imposing strong assumptions such as Gaussianity or *M*-dependence. We propose a novel nonparametric test that integrates weak dependence theory with high-dimensional covariance structure estimation, yielding a computationally efficient and theoretically justified test statistic. Its asymptotic normality is rigorously established under mild weak dependence conditions. The method substantially reduces computational complexity, making it scalable to large-scale, high-dimensional time series. Extensive simulations demonstrate superior statistical power and computational efficiency compared to existing approaches. Our key contribution is the first establishment of an asymptotically normal theoretical framework for high-dimensional mean testing under broad weak dependence assumptions—providing a generalizable methodological foundation for subsequent high-dimensional time-series inference.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Non-convex Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

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.

Problem

• Develops a test for high-dimensional mean with temporal dependence
• Establishes asymptotic normality without restrictive distributional assumptions
• Reduces computational complexity for large-scale temporal data applications

Innovation

• Novel high-dimensional mean test for temporal dependent data
• Asymptotic normality without restrictive distribution assumptions
• Reduced computational complexity for large-scale applications