We establish central limit theorems for principal eigenvalues and eigenvectors under a large factor model setting, and develop two-sample tests of both principal eigenvalues and principal eigenvectors. One important application is to detect structural breaks in large factor models. Compared with existing methods for detecting structural breaks, our tests provide unique insights into the source of structural breaks because they can distinguish between individual principal eigenvalues and/or eigenvectors. We demonstrate the application by comparing the principal eigenvalues and principal eigenvectors of S\&P500 Index constituents' daily returns over different years.

翻译：我们在大因子模型设定下建立了主特征值与特征向量的中心极限定理，并开发了同时针对主特征值与主特征向量的双样本检验。该方法的重要应用之一是检测大因子模型中的结构突变。与现有结构突变检测方法相比，我们的检验能够区分单个主特征值和/或特征向量的变化，从而为结构突变的来源提供独特见解。通过比较标普500指数成分股不同年份日度收益率的主特征值与特征向量，我们展示了该方法的实际应用。