Sungyoon Lee, Sokbae Lee
arXiv 22 May 2023 · Mathematics — Statistics Theory
arXiv:2305.12883 · PDF · DOI · OpenAlex · Extracted main text
In recent years, there has been a significant growth in research focusing on minimum $\ell_2$ norm (ridgeless) interpolation least squares estimators. However, the majority of these analyses have been limited to an unrealistic regression error structure, assuming independent and identically distributed errors with zero mean and common variance. In this paper, we explore prediction risk as well as estimation risk under more general regression error assumptions, highlighting the benefits of overparameterization in a more realistic setting that allows for clustered or serial dependence. Notably, we establish that the estimation difficulties associated with the variance components of both risks can be summarized through the trace of the variance-covariance matrix of the regression errors. Our findings suggest that the benefits of overparameterization can extend to time series, panel and grouped data.
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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 | Dobriban, E. and S. Wager (2018) High-dimensional asymptotics of prediction: Ridge regression and classification | 0.874 | 6 | 2 | 100% |
| 2 | Hastie, T., A. Montanari, S. Rosset, and R. J. Tibshirani (2022) Surprises in high-dimensional ridgeless least squares interpolation | 0.874 | 5 | 2 | 100% |
| 3 | Chinot, G. and M. Lerasle (2023) On the robustness of the minimum $_2$ interpolator | 0.644 | 4 | 1 | 100% |
| 4 | Richards, D., J. Mourtada, and L. Rosasco (2021) Asymptotics of ridge (less) regression under general source condition | 0.644 | 2 | 2 | 100% |
| 5 | Chinot, G., M. Löffler, and S. van de Geer (2022) On the robustness of minimum norm interpolators and regularized empirical risk minimizers | 0.511 | 2 | 1 | 100% |
| 6 | Bartlett, P. L., P. M. Long, G. Lugosi, and A. Tsigler (2020) Benign overfitting in linear regression | 0.511 | 2 | 1 | 100% |
| 7 | Silverstein, J. W. and Z. Bai (1995) On the empirical distribution of eigenvalues of a class of large dimensional random matrices | 0.511 | 2 | 1 | 100% |
| 8 | Tsigler, A. and P. L. Bartlett (2023) Benign overfitting in ridge regression | 0.511 | 2 | 1 | 100% |
| 9 | Abadie, A., A. Diamond, and J. Hainmueller (2010) Synthetic control methods for comparative case studies: Estimating the effect of california’s tobacco control program | 0.405 | 1 | 1 | 100% |
| 10 | Ruggles, S., S. Flood, M. Sobek, D. Backman, A. Chen, G. Cooper, S.… (2024) IPUMS USA: Version 15.0 [dataset] | 0.405 | 1 | 1 | 100% |
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