论文标题
大维渔民矩阵和应用的尖峰特征值的不变性原理和CLT
Invariance principle and CLT for the spiked eigenvalues of large-dimensional Fisher matrices and applications
论文作者
论文摘要
本文旨在得出大维尖刺的渔民矩阵的尖峰特征值的渐近分布，而没有高斯假设以及对协方差矩阵的限制性假设。我们首先建立了Fisher Matrix尖刺特征值的不变性原理。也就是说，我们表明，尖刺特征值的限制分布在满足某些条件的大量人群分布中是不变的。使用不变性原则，我们进一步为尖刺特征值建立了一个中心极限定理（CLT）。作为一些有趣的应用，我们使用CLT来得出线性模型中线性假设的ROY最大根检验的功率函数以及信号检测中的测试。我们进行了一些蒙特卡洛模拟，以将拟议的测试与现有测试进行比较。
This paper aims to derive asymptotical distributions of the spiked eigenvalues of the large-dimensional spiked Fisher matrices without Gaussian assumption and the restrictive assumptions on covariance matrices. We first establish invariance principle for the spiked eigenvalues of the Fisher matrix. That is, we show that the limiting distributions of the spiked eigenvalues are invariant over a large class of population distributions satisfying certain conditions. Using the invariance principle, we further established a central limit theorem (CLT) for the spiked eigenvalues. As some interesting applications, we use the CLT to derive the power functions of Roy Maximum root test for linear hypothesis in linear models and the test in signal detection. We conduct some Monte Carlo simulation to compare the proposed test with existing ones.
