长记忆时间序列的高维高斯图模型检验
High-dimensional Gaussian Graphical Model Testing for Long-Memory Time Series
- University of Chicago（芝加哥大学）
- University of Illinois Chicago（伊利诺伊大学芝加哥分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对长记忆高维时间序列，提出数据自适应的条件独立性检验统计量，建立有限样本高斯近似界，采用块自助法，并应用于fMRI数据分析脑功能连接。
AI中文摘要：
许多现实世界的高维时间序列表现出长记忆性，但在此情形下的高斯图模型检验仍研究不足。我们开发了一个直接、数据自适应的检验统计量，用于评估平稳高斯时间序列图结构中的条件独立性。我们为该统计量建立了有限样本的Berry-Esseen型高斯近似界，该界同时适用于短记忆和长记忆时间序列。该检验过程完全数据自适应，采用块自助法，我们为其提供了有限样本有效性结果，包括在超高维情形下，并可扩展到两样本检验中以比较图结构。我们还开发了一个基于一致性增强的统计量修正，并证明此类检验在大小和功效上均达到渐近一致性。我们将所提出的方法应用于真实世界的fMRI数据，以理解大脑在不同时期的功能连接性。
英文摘要：
Many real-world high-dimensional time series exhibit long-memory, but Gaussian graphical model testing in this regime remains understudied. We develop a direct, data-adaptive test statistic for assessing conditional independence in the graph structure of stationary Gaussian time series. We establish a finite-sample, Berry--Esseen type Gaussian approximation bound for the statistic, which applies to both short-memory and long-memory time series. The testing procedure is fully data-adaptive using block bootstrap method, on which we provide a finite-sample validity result including in the ultra-high-dimensional scenario, and can be extended to comparing graphical structures in two-sample tests. We also develop a consistency-empowered correction to the statistic and show that such tests attain asymptotic consistency in both size and power. Our proposed method is applied to a real-world fMRI data to understand functional connectivities within brain in different periods.
