Christian Brownlees, Guðmundur Stefán Guðmundsson, Yaping Wang
arXiv 5 Sep 2024 · Econometrics
arXiv:2409.03606 · PDF · DOI · OpenAlex · Extracted main text
This paper establishes bounds on the predictive performance of empirical risk minimization for principal component regression. Our analysis is nonparametric, in the sense that the relation between the prediction target and the predictors is not specified. In particular, we do not rely on the assumption that the prediction target is generated by a factor model. In our analysis we consider the cases in which the largest eigenvalues of the covariance matrix of the predictors grow linearly in the number of predictors (strong signal regime) or sublinearly (weak signal regime). The main result of this paper shows that empirical risk minimization for principal component regression is consistent for prediction and, under appropriate conditions, it achieves near-optimal performance in both the strong and weak signal regimes.
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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, J. and Ng, S (2002) Determining the Number of Factors in Approximate Factor Models | 1.000 | 6 | 3 | 100% |
| 2 | Fan, J., Liao, Y., and Mincheva, M (2011) High Dimensional Covariance Matrix Estimation in Approximate Factor Models | 1.000 | 5 | 3 | 100% |
| 3 | Brownlees, C. and Gumundsson, G. S (2025) Performance of empirical risk minimization for linear regression with dependent data self | 0.950 | 7 | 4 | 86% |
| 4 | Bai, J. and Ng, S (2023) Approximate factor models with weaker loadings | 0.737 | 3 | 2 | 100% |
| 5 | Fan, J., Liao, Y., and Mincheva, M (2013) Large covariance estimation by thresholding principal orthogonal complements | 0.737 | 3 | 2 | 100% |
| 6 | Bai, J (2003) Inferential theory for factor models of large dimensions | 0.644 | 2 | 2 | 100% |
| 7 | Jiang, W. and Tanner, M. A (2010) Risk minimization for time series binary choice with variable selection | 0.644 | 2 | 2 | 100% |
| 8 | Lecué, G. and Mendelson, S (2016) Performance of empirical risk minimization in linear aggregation | 0.644 | 2 | 2 | 100% |
| 9 | Lecué, G. and Mendelson, S (2018) Regularization and the small-ball method i: Sparse recovery | 0.644 | 2 | 2 | 100% |
| 10 | Mendelson, S (2018) Learning without concentration for general loss functions | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 45 scored citations.