在持续的纵横比异质性下采用自适应权重的分布式尖峰特征值在线估计
Distributed Online Estimation of Spiked Eigenvalues with Adaptive Weighting under Persistent Aspect Ratio Heterogeneity
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中文总结 AI 辅助
针对多节点异质性有效样本量的尖峰协方差特征值在线估计问题，提出先校正再聚合的分布式框架，实现高效低通信成本的在线推断与系统性风险实时跟踪。
中文摘要 AI 辅助
我们研究了来自L个节点的观测值的尖峰协方差特征值在线估计问题，这些节点具有异质性且持续存在的有效样本量。在比例高维区域中，局部瑞利统计量会被节点特定的纵横比$c_{\ell,t}=p/N^{\mathrm{eff}}_{\ell,t}$确定性地扭曲，而直接聚合未校正的统计量会收敛到错误的极限。我们提出了“先校正再聚合”框架，其中每个节点通过逆瑞利传递图消除其确定性偏差，服务器基于可预测的波动指标使用自适应软最大权重融合校正后的估计值，每个活跃节点每轮仅传输$O(k)$个标量。我们证明了全局估计量的一致性和渐近正态性，从而实现有效的在线推断，并推导了非渐近边界，量化了精度如何随节点数量及其有效样本量的增加而提升。自适应权重实现了与 oracle 逆方差权重相当的方差减少，证实了这种数据驱动的构造几乎是高效的。模拟研究验证了这些性质。将其应用于跨场所监测主导市场因子的案例表明，该方法可实时跟踪系统性风险，同时相较于集中式合并方法大幅降低了通信成本。
英文摘要
We study online estimation of spiked covariance eigenvalues from observations distributed across $L$ nodes with heterogeneous and persistent effective sample sizes. In the proportional high-dimensional regime, local Rayleigh statistics are deterministically distorted by node-specific aspect ratios $c_{\ell,t}=p/N^{\mathrm{eff}}_{\ell,t}$, and direct aggregation of uncorrected statistics converges to the wrong limit. We propose a correct-then-aggregate framework in which each node removes its deterministic bias via an inverse Rayleigh transfer map, and the server fuses corrected estimates using adaptive soft-max weights based on predictable fluctuation metrics, transmitting only $O(k)$ scalars per active node per round. We establish consistency and asymptotic normality of the global estimator, enabling valid online inference, and derive non-asymptotic bounds quantifying how accuracy improves with the number of nodes and their effective sample sizes. The adaptive weights achieve variance reduction comparable to oracle inverse-variance weighting, confirming the data-driven construction is nearly efficient. Simulation studies validate these properties. An application to cross-venue monitoring of a dominant market factor shows the method tracks systemic risk in real time while substantially reducing communication cost relative to a centralized pooled approach.
