Independent Component Analysis With Heavy Tails Using Distance Covariance
本文研究当源信号具有无限方差（重尾分布）时，如何用距离协方差作为目标函数进行独立成分分析，并证明了该方法的相合性，还扩展到含噪声的ICA模型，适用于金融时间序列等场景。
ABSTRACT Independent Component Analysis (ICA) is a popular tool used for blind source separation and has found application in fields such as financial time series, signal processing, feature extraction, and brain imaging. Inspired by modeling a macroeconomic time series that has components with heavy tails, we consider the ICA problem with an infinite variance source. Many of the ICA procedures require the existence of a finite second or even fourth moment. Distance covariance is a measure of dependence that has become an increasingly popular choice as an objective function in the ICA setting. Unfortunately, the standard weight function used in distance covariance requires a finite variance assumption when applied in the ICA framework. The objective of this paper is to derive consistency when using the distance covariance applied to the infinite variance case. Extensions to the ICA model with noise, which has a direct application to time series models when testing independence of residuals based on their estimated counterparts, are also considered.