高维相关性矩阵的两步估计器
Andrés García-Medina1, Salvatore Miccichè2, Rosario N Mantegna3
1Centro de Investigación en Matemáticas, Unidad Monterrey, Av. Alianza Centro 502, PIIT 66628, Apodaca, Nuevo León, México and Consejo Nacional de Humanidades, Ciencias y Tecnologías, Av. Insurgentes Sur 1582, Col. Crédito Constructor 03940, Ciudad de México, México.
Physical review. E
|November 18, 2023
概括
层次集群估计器 (HCE) 在分析高维高斯模型时优于旋转不变估计器 (RIE). 结合收缩和HCE的两步估计器最好在块和嵌套模型中确定过样本的交叉相关性.
科学领域:
- 多变量统计学 多变量统计学
- 高维数据分析 高维数据分析
- 机器学习 机器学习
背景情况:
- 随机多变量高斯模型对于理解复杂的数据结构至关重要.
- 在高维度中分析样本交叉相关性矩阵带来了重大的统计挑战.
- 像旋转不变估计器 (RIE) 这样的现有方法在准确捕捉底层相关性方面存在局限性.
研究的目的:
- 在高维高斯模型中调查和比较样本交叉相关性矩阵的不同估计器的性能.
- 在各种损失函数下,评估等级集群估计器 (HCE) 与RIE的有效性.
- 为区块对角线和层次嵌套模型开发改进的估计策略.
主要方法:
- 进行了数值模拟来分析块对角和层次嵌套的随机多变量高斯模型.
- 过样本交叉相关性矩阵与使用RIEs和HCEs的人口交叉相关性矩阵的比较.
- 根据多个损失函数进行评估,并引入结合非线性收缩和HCE的两步估计器.
主要成果:
- 层次集群估计器 (HCE) 在多个损失函数的大型,有限的样本大小中通常表现优于旋转不变估计器 (RIE).
- 对于块模型和层次嵌套块模型,双步估计器表现出优异的性能.
- 将最先进的非线性收缩与HCE结合起来,证明在这些特定模型结构中确定过样本交叉相关性是最有效的.
结论:
- HCE 提供了比 RIE 更强大的方法来估计高维高斯设置中的交叉相关性.
- 拟议的两步估计策略显著提高了结构化模型的相关性矩阵估计的准确性.
- 这项研究为选择和开发高维数据分析中先进的统计方法提供了宝贵的见解.
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