Pervasive cross-section dependence is increasingly recognized as an appropriate characteristic of economic data and the approximate factor model provides a useful framework for analysis. Assuming a strong factor structure, early work established convergence of the principal component estimates of the factors and loadings to a rotation matrix. This paper shows that the estimates are still consistent and asymptotically normal for a broad range of weaker factor loadings, albeit at slower rates and under additional assumptions on the sample size. Standard inference procedures can be used except in the case of extremely weak loadings which has encouraging implications for empirical work. The simplified proofs are of independent interest.

翻译：人们日益认识到,跨部门依赖性是经济数据的适当特征,近似要素模型为分析提供了有用的框架;假设要素结构强大,早期工作就确定了要素主要组成部分估计数的趋同和对轮值矩阵的负荷;本文件表明,对于一系列较弱要素负荷而言,这些估计数仍然是一致的,而且无异于正常的,尽管其速度较慢,而且根据对抽样规模的额外假设;可以使用标准推论程序,除非负荷极弱,这对经验性工作有令人鼓舞的影响;简化证据具有独立的利益。