标题： 广义尖峰模型下四个线性假设检验统计量的渐近分布 显示英文标题

标题： Asymptotic distributions of four linear hypotheses test statistics under generalized spiked model

摘要： 在本文中，我们建立了大维广义尖峰样本协方差矩阵的线性谱统计量（LSSs）的中心极限定理（CLT），其中尖峰特征值可能是有界的或发散到无穷大。 基于该定理，我们推导了广义尖峰模型下线性假设检验统计量的渐近分布，包括Wilks似然比检验统计量U、Lawley-Hotelling迹检验统计量W以及Bartlett-Nanda-Pillai迹检验统计量V。 由于检验函数的复杂性，我们在计算中的围道积分的显式解通常难以求得。 为了解决这个问题，我们采用泰勒级数展开来近似渐近情况下的理论结果。 我们还推导了上述三种检验准则的渐近功效函数，并在特定情况下与Roy的最大根检验进行了比较。 最后，进行了数值模拟以验证我们渐近近似的准确性。 显示英文摘要

摘要： In this paper, we establish the Central Limit Theorem (CLT) for linear spectral statistics (LSSs) of large-dimensional generalized spiked sample covariance matrices, where the spiked eigenvalues may be either bounded or diverge to infinity. Building upon this theorem, we derive the asymptotic distributions of linear hypothesis test statistics under the generalized spiked model, including Wilks' likelihood ratio test statistic U, the Lawley-Hotelling trace test statistic W, and the Bartlett-Nanda-Pillai trace test statistic V. Due to the complexity of the test functions, explicit solutions for the contour integrals in our calculations are generally intractable. To address this, we employ Taylor series expansions to approximate the theoretical results in the asymptotic regime. We also derive asymptotic power functions for three test criteria above, and make comparisons with Roy's largest root test under specific scenarios. Finally, numerical simulations are conducted to validate the accuracy of our asymptotic approximations.