Rank regularized estimation of approximate factor models
Rank regularized estimation of approximate factor models
复制标题
DOI：
10.1016/j.jeconom.2019.04.021
复制
发表时间：
2019-09
影响因子：
6.3
通讯作者：
Jushan Bai;Serena Ng
中科院分区：
文献类型：
--
作者：
Jushan Bai;Serena Ng
众所周知，在一个大的面板数据的共同因素，可以一致地估计的主成分的方法，主成分可以通过迭代最小二乘回归构建。用岭回归代替最小二乘，结果证明具有从公共分量中去除与小奇异值相关的因子的贡献的效果。该方法已在机器学习文献中用于恢复低秩矩阵。我们从估计近似因子模型的角度来研究这个过程。在秩约束条件下，通过奇异值超过阈值的因子所跨越的空间来估计公共分量。对最小秩和简约性的期望导致了选择因子数量的数据依赖性惩罚。新准则比现有的确定性惩罚更保守，并且当因子的标称数量因弱因子或大测量噪声的存在而膨胀时是适当的。我们提供的渐近结果，可用于检验经济假设。
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 removing the contribution of factors associated with small singular values from the common component. The method has been used in the machine learning literature to recover low-rank matrices. We study the procedure from the perspective of estimating an approximate factor model. Under the rank-constraint, the common component is estimated by the space spanned by factors whose singular values exceed a threshold. The desire for minimum rank and parsimony lead to a data-dependent penalty for selecting the number of factors. The new criterion is more conservative than the existing deterministic penalties and is appropriate when the nominal number of factors is inflated by the presence of weak factors or large measurement noise. We provide asymptotic results that can be used to test economic hypotheses.