Rank regularized estimation of approximate factor models

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 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. (C) 2019 Elsevier B.V. All rights reserved.