四阶矩与独立分量分析
Fourth Moments and Independent Component Analysis
摘要：
在独立分量分析中，假设所观察到的随机向量的分量是潜在独立随机变量的线性组合，并且目标是然后找到返回到这些独立分量的变换矩阵的估计。在工程文献中，有几个传统的估计程序的基础上使用的四阶矩，如FOBI（四阶盲识别），JADE（联合近似对角化的特征矩阵），和FastICA，但这些估计的统计特性并不为人所知。本文详细讨论了基于四阶矩的各种独立分量泛函，从相应的最优化问题出发，导出了估计方程和估计算法，并得到了估计的渐近统计性质。宽独立分量模型估计的渐近方差的比较表明，在大多数情况下，JADE和FastICA的对称版本比他们的竞争对手表现得更好。
英文摘要：
In independent component analysis it is assumed that the components of the observed random vector are linear combinations of latent independent random variables, and the aim is then to find an estimate for a transformation matrix back to these independent components. In the engineering literature, there are several traditional estimation procedures based on the use of fourth moments, such as FOBI (fourth order blind identification), JADE (joint approximate diagonalization of eigenmatrices), and FastICA, but the statistical properties of these estimates are not well known. In this paper various independent component functionals based on the fourth moments are discussed in detail, starting with the corresponding optimization problems, deriving the estimating equations and estimation algorithms, and finding asymptotic statistical properties of the estimates. Comparisons of the asymptotic variances of the estimates in wide independent component models show that in most cases JADE and the symmetric version of FastICA perform better than their competitors.
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