发表机构
Aarhus University（奥胡斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对大型面板数据中分组球形误差结构假设过于严格的问题，本文提出基于极端特征值和随机矩阵理论的拟合优度检验方法，以评估偏离假设的实际相关性，并在有限样本中实现准确尺寸控制与良好功效。
AI 中文摘要
大型数据面板的分析在计量经济学及其他领域具有重要意义。针对此类数据的预测和推断方法通常依赖于对误差协方差结构的简化模型假设。一个便捷的假设是我们所称的分组球形性：即误差在个体间不相关，并在特定组内具有恒定方差。尽管该假设在理论上有效，但在大型面板中，分组球形性在实践中往往过于严格而难以应用。因此，我们开发了新的定量推断工具，以检验偏离该模型假设是否具有实际相关性。我们的方法涵盖大型数据矩阵和回归面板，在横截面维度与样本量成比例的情况下适用。该理论基于经验协方差矩阵极端特征值的分析，并利用了随机矩阵理论的最新进展。数值实验证明了在有限样本中准确的尺寸控制和良好的功效。
英文摘要
The analysis of large data panels is important in econometrics and beyond. Prediction and inference methods for such data typically rely on simplifying model assumptions for the covariance structure of errors. One convenient assumption is what we call groupwise sphericity: that errors are uncorrelated across individuals and have constant variance within certain groups. While theoretically useful, in large panels groupwise sphericity is often too restrictive to apply in practice. We therefore develop new quantitative inference tools to test whether deviations from this model assumption are practically relevant. Our approach covers both large-dimensional data matrices and regression panels, in a regime where the cross-sectional dimension is proportional to the sample size. The theory is based on the analysis of extreme eigenvalues of the empirical covariance matrix and uses recent advances in random matrix theory. Numerical experiments demonstrate accurate size control and good power in finite samples.
