A bootstrap method for spectral statistics in high-dimensional elliptical models
A bootstrap method for spectral statistics in high-dimensional elliptical models
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DOI：
10.1214/23-ejs2140
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发表时间：
2022-09
影响因子：
1.1
通讯作者：
Si-Ying Wang;Miles E. Lopes
中科院分区：
文献类型：
--
作者：
Si-Ying Wang;Miles E. Lopes
虽然有大量关于高维样本协方差矩阵特征值的文献，但其中大部分都是专门针对独立分量（IC）模型的-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，椭圆模型的背景下所知甚少，它违反了IC模型的独立结构，并表现出截然不同的统计现象。特别是，很少有人知道的范围内的引导方法做推断与光谱统计在高维椭圆模型。为了填补这一空白，我们展示了如何引导的方法，以前开发的IC模型可以扩展到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的线性谱统计，这在多元分析中发挥了重要作用的分布。我们还提供了实证结果表明，所提出的方法表现良好的各种非线性谱统计。
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.