EconBase
← All papers

Prediction Risk and Estimation Risk of the Ridgeless Least Squares Estimator under General Assumptions on Regression Errors

Sungyoon Lee, Sokbae Lee

arXiv 22 May 2023 · Mathematics — Statistics Theory

arXiv:2305.12883 · PDF · DOI · OpenAlex · Extracted main text

Abstract

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.

Citation extraction

29
references
46
in-text mentions
29
distinct cited
0
self-citations
6,443
main-text words

appendix boundary found by appendix_command · 72% of the source is main text. Read the extracted text to check this.

Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Dobriban, E. and S. Wager (2018) High-dimensional asymptotics of prediction: Ridge regression and classification0.87462100%
2Hastie, T., A. Montanari, S. Rosset, and R. J. Tibshirani (2022) Surprises in high-dimensional ridgeless least squares interpolation0.87452100%
3Chinot, G. and M. Lerasle (2023) On the robustness of the minimum $_2$ interpolator0.64441100%
4Richards, D., J. Mourtada, and L. Rosasco (2021) Asymptotics of ridge (less) regression under general source condition0.64422100%
5Chinot, G., M. Löffler, and S. van de Geer (2022) On the robustness of minimum norm interpolators and regularized empirical risk minimizers0.51121100%
6Bartlett, P. L., P. M. Long, G. Lugosi, and A. Tsigler (2020) Benign overfitting in linear regression0.51121100%
7Silverstein, J. W. and Z. Bai (1995) On the empirical distribution of eigenvalues of a class of large dimensional random matrices0.51121100%
8Tsigler, A. and P. L. Bartlett (2023) Benign overfitting in ridge regression0.51121100%
9Abadie, A., A. Diamond, and J. Hainmueller (2010) Synthetic control methods for comparative case studies: Estimating the effect of california’s tobacco control program0.40511100%
10Ruggles, S., S. Flood, M. Sobek, D. Backman, A. Chen, G. Cooper, S.… (2024) IPUMS USA: Version 15.0 [dataset]0.40511100%

Showing the top 10 of 29 scored citations.