论文标题
用于高维椭圆模型中光谱统计的引导法方法
A Bootstrap Method for Spectral Statistics in High-Dimensional Elliptical Models
论文作者
论文摘要
尽管关于高维样品协方差矩阵的特征值有广泛的文献，但其中大部分专门针对独立组件（IC）模型，其中观测值表示为具有独立条目的随机向量的线性变换。相比之下，在椭圆模型的背景下，较少的知识是违反了IC模型的独立性结构，并且表现出完全不同的统计现象。特别是，对于在高维椭圆模型中使用光谱统计的推理范围的范围知之甚少。为了填补这一空白，我们展示了以前如何为IC模型开发的引导方法如何扩展以处理椭圆模型的不同属性。在这种情况下，我们的主要理论结果保证了所提出的方法始终近似线性频谱统计的分布，这在多元分析中起着基本作用。我们还提供了经验结果，表明所提出的方法在各种非线性光谱统计中都表现良好。
Although there is an extensive literature on the eigenvalues of high-dimensional sample covariance matrices, much of it is specialized to independent components (IC) models -- in which observations are represented as linear transformations of random vectors with independent entries. By contrast, less is known in the context of elliptical models, which violate the independence structure of IC models and exhibit quite different statistical phenomena. In particular, very little is known about the scope of bootstrap methods for doing inference with spectral statistics in high-dimensional elliptical models. To fill this gap, we show how a bootstrap approach developed previously for IC models can be extended to handle the different properties of elliptical models. Within this setting, our main theoretical result guarantees that the proposed method consistently approximates the distributions of linear spectral statistics, which play a fundamental role in multivariate analysis. We also provide empirical results showing that the proposed method performs well for a variety of nonlinear spectral statistics.
