摘要翻译：
主成分法可以一致地估计大数据面中的公因子，主成分可以通过迭代最小二乘回归来构造。用岭回归代替最小二乘结果表明，它的作用是缩小公共分量的奇异值，并可能降低其秩。该方法用于机器学习文献中的低秩矩阵恢复。我们从估计一个最小秩近似因子模型的角度研究了这一过程。我们证明了约束因子估计是有偏的，但在均方误差方面可以更有效。等级考虑建议在选择因素的数量时有一个依赖于数据的惩罚。当由于弱因素或测量噪声的存在而使标称因素数膨胀时，新判据更加保守。该框架被扩展为包含对载荷的先验线性约束。我们提供了可以用来检验经济假说的渐近结果。
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英文标题：
《Principal Components and Regularized Estimation of Factor Models》
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作者：
Jushan Bai and Serena Ng
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最新提交年份：
2017
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分类信息：

一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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英文摘要：
  It is known that the common factors in a large panel of data can be consistently estimated by the method of principal components, and principal components can be constructed by iterative least squares regressions. Replacing least squares with ridge regressions turns out to have the effect of shrinking the singular values of the common component and possibly reducing its rank. The method is used in the machine learning literature to recover low-rank matrices. We study the procedure from the perspective of estimating a minimum-rank approximate factor model. We show that the constrained factor estimates are biased but can be more efficient in terms of mean-squared errors. Rank consideration suggests a data-dependent penalty for selecting the number of factors. The new criterion is more conservative in cases when the nominal number of factors is inflated by the presence of weak factors or large measurement noise. The framework is extended to incorporate a priori linear constraints on the loadings. We provide asymptotic results that can be used to test economic hypotheses.
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PDF链接：
https://arxiv.org/pdf/1708.08137