Independent Component Analysis (ICA) offers an effective data-driven approach for blind source extraction encountered in many signal and image processing problems. Although many ICA methods have been developed, they have received relatively little attention in the statistics literature, especially in terms of rigorous theoretical investigation for statistical inference. The current paper aims at narrowing this gap and investigates the statistical sampling properties of the colorICA (cICA) method. The cICA incorporates the correlation structure within sources through parametric time series models in the frequency domain and outperforms several existing ICA alternatives numerically. We establish the consistency and asymptotic normality of the cICA estimates, which then enables statistical inference based on the estimates. These asymptotic properties are further validated using simulation studies.

中文翻译：

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颜色独立分量分析的采样特性

独立分量分析 (ICA) 为在许多信号和图像处理问题中遇到的盲源提取提供了一种有效的数据驱动方法。尽管已经开发了许多 ICA 方法，但它们在统计文献中受到的关注相对较少，特别是在统计推断的严格理论研究方面。目前的论文旨在缩小这一差距并研究 colorICA (cICA) 方法的统计采样特性。cICA 通过频域中的参数化时间序列模型将源内的相关结构纳入其中，并在数值上优于几种现有的 ICA 替代方案。我们建立了 cICA 估计值的一致性和渐近正态性，然后可以基于估计值进行统计推断。