大维数近似因子模型的简单证明
Simpler Proofs for Approximate Factor Models of Large Dimensions
摘要：
近似因子模型的估计越来越多地用于实证工作中。它们的理论性质，研究了大约20年前，也奠定了基础工作，分析大规模的面板数据模型与横截面的依赖。本文提出了简化证明的估计使用交替旋转矩阵，利用低秩矩阵的性质，以及奇异值分解的数据，除了其协方差结构。这些简化有助于解释结果，并为新进入该领域的研究人员提供更友好的介绍。提供了新的结果，允许对因子模型施加线性限制。
英文摘要：
Estimates of the approximate factor model are increasingly used in empirical work. Their theoretical properties, studied some twenty years ago, also laid the ground work for analysis on large dimensional panel data models with cross-section dependence. This paper presents simplified proofs for the estimates by using alternative rotation matrices, exploiting properties of low rank matrices, as well as the singular value decomposition of the data in addition to its covariance structure. These simplifications facilitate interpretation of results and provide a more friendly introduction to researchers new to the field. New results are provided to allow linear restrictions to be imposed on factor models.
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