Principal Components and Regularized Estimation of Factor Models

By Jushan Bai, Serena Ng. 2017

24 citations recorded by the source corpus.

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.

Subfields: Computational Mechanics, Economics and Econometrics, Statistics and Probability, Statistical Learning Theory

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Citations in the corpus

Estimating latent asset-pricing factors (2018, background): “Bai and Ng (2017) develop the statistical theory for robust principal components.”
On factor models with random missing: EM estimation, inference, and cross validation (2020, background): “As in Bai and Ng (2017), we want to establish the connection between the usual principal component (PC) estimators of the factors and factor loadings and the SVD estimators.”
Nuclear norm regularized estimation of panel regression models (2018, unknown): “More recently, nuclear norm penalization has also been used in the econometrics literature: Bai and Ng (2017, 2019) use it to improve estimation in a pure factor model.”
Feasible generalized least squares for panel data with cross-sectional and serial correlations (2019, methodology): “This method, in the FGLS setting, is equivalent to “banding”, previously proposed by Bickel and Levina (2008b) for estimating large covariance matrices. We apply it to banding out off-diagonal N ×N blocks that are far from the diagonal block. In addition, to control for the cross-sectional correlati”