论文标题
高维相关矩阵的两步估计器
Two-step estimators of high dimensional correlation matrices
论文作者
论文摘要
我们通过研究其样品互相关矩阵上的高尺寸，研究了块对角线和分层嵌套的随机多变量高斯模型。通过执行数值模拟，我们通过使用几个损耗函数下的几个旋转不变的估计器（RIE）（RIE）（RIE）（RIE）（RIE）（RIE）（RIE）（RIE）和分层聚类估计器（HCE）将过滤样品的互相关与种群互相关矩阵进行了比较。我们表明，在很大但有限的样本量下，通过RIE估计器过滤的样品互相关通常超过HCE估计器的几个损耗函数。我们还表明，对于块模型，对于层次嵌套模型，通过引入将最新的非线性收缩模型与层次群集估计器结合的两步估计器来实现过滤后样品互相关的最佳测定。
We investigate block diagonal and hierarchical nested stochastic multivariate Gaussian models by studying their sample cross-correlation matrix on high dimensions. By performing numerical simulations, we compare a filtered sample cross-correlation with the population cross-correlation matrices by using several rotationally invariant estimators (RIE) and hierarchical clustering estimators (HCE) under several loss functions. We show that at large but finite sample size, sample cross-correlation filtered by RIE estimators are often outperformed by HCE estimators for several of the loss functions. We also show that for block models and for hierarchically nested block models the best determination of the filtered sample cross-correlation is achieved by introducing two-step estimators combining state-of-the-art non-linear shrinkage models with hierarchical clustering estimators.
