arXiv 27 Aug 2017 · Statistics — Methodology · 13 citations (OpenAlex)
arXiv:1708.08137 · PDF · DOI · OpenAlex · Extracted main text
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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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Bai \ Ng (2002) Determining the number of factors in approximate factor models, Econometrica 70:1: 191–221 | 1.000 | 6 | 4 | 100% |
| 2 | Hastie, Mazumder, Lee \ Zadeh (2015) Matrix completion and low rank svd via fast alternating least squares, Journal of Machine Learning Research 16: 3367–3402 | 1.000 | 5 | 3 | 100% |
| 3 | Fan, Liao \ Mincheva (2013) Large covariance estimation by thresholding principal orthogonal complements, Journal of Royal Statistical Society, Series B 75(… | 0.843 | 3 | 3 | 100% |
| 4 | Agarwal, Negahban \ Wainwright (2012) Noisy matrix decompositions via convex relation: Optimal rates in high dimensions, Annals of Statistics 40(2): 1171–1197 | 0.811 | 4 | 2 | 100% |
| 5 | Bai (2003) Inferential theory for factor models of large dimensions, Econometrica 71:1: 135–172 self | 0.811 | 4 | 2 | 100% |
| 6 | Candes, Li, Ma \ Wright (2011) Robust principal compoennt analysis, Journal of the ACM 58(3): Article 11 | 0.737 | 3 | 2 | 100% |
| 7 | ten Berge \ Kiers (1991) A numerical approach to the exact and the approximate minimum rank of a covariance matrix, Psychometrika 56: 309–315 | 0.737 | 3 | 2 | 100% |
| 8 | Bai \ Ng (2006) Confidence intervals for diffusion index forecasts and inference with factor-augmented regressions, Econometrica 74:4: 1133–1150 | 0.644 | 2 | 2 | 100% |
| 9 | Bertsimas, Copenhaver \ Mazumder (2016) Certifiably optimal low rank factor analysis | 0.644 | 2 | 2 | 100% |
| 10 | Shen \ Huang (2008) Sparse principal component analysis via regularized low rank matrix approximations, Journal of Multivariate Analysis 99: 1015–1034 | 0.644 | 2 | 2 | 100% |
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