论文标题
对高维尖刺模型及其应用中尖峰的通用测试
A universal test on spikes in a high-dimensional generalized spiked model and its applications
论文作者
论文摘要
本文旨在测试广义尖峰协方差矩阵中的尖峰数量，其尖峰特征值可能比非刺激性峰值大或小。对于高维问题，我们首先提出了一个通用测试统计量，并通过随机矩阵理论得出其中心限制定理，而无需高斯群体约束。然后，我们应用结果来估计噪声方差并测试广义尖峰模型中最小根的平等。模拟研究表明，提出的测试方法的尺寸正确，功率结果表明我们统计学对与高斯人群的偏差的稳健性。此外，与现有方法相比，我们对噪声差异的估计器导致的平均绝对错误和平方误差要小得多。与先前开发的方法相反，我们消除了种群协方差矩阵的对角线或斜角对角线形式的严格条件，并将工作扩展到更广泛的范围，而无需假设正态性。因此，提出的方法更适合实际问题。
This paper aims to test the number of spikes in a generalized spiked covariance matrix, the spiked eigenvalues of which may be extremely larger or smaller than the non-spiked ones. For a high-dimensional problem, we first propose a general test statistic and derive its central limit theorem by random matrix theory without a Gaussian population constraint. We then apply the result to estimate the noise variance and test the equality of the smallest roots in generalized spiked models. Simulation studies showed that the proposed test method was correctly sized, and the power outcomes showed the robustness of our statistic to deviations from a Gaussian population. Moreover, our estimator of the noise variance resulted in much smaller mean absolute errors and mean squared errors than existing methods. In contrast to previously developed methods, we eliminated the strict conditions of diagonal or block-wise diagonal form of the population covariance matrix and extend the work to a wider range without the assumption of normality. Thus, the proposed method is more suitable for real problems.
