Christian Brownlees, Guðmundur Stefán Guðmundsson
arXiv 25 Apr 2021 · Econometrics · publishedEconometric Theory (2021) · 1 citations (OpenAlex)
arXiv:2104.12127 · PDF · DOI · OpenAlex · Extracted main text
This paper establishes bounds on the performance of empirical risk minimization for large-dimensional linear regression. We generalize existing results by allowing the data to be dependent and heavy-tailed. The analysis covers both the cases of identically and heterogeneously distributed observations. Our analysis is nonparametric in the sense that the relationship between the regressand and the regressors is not specified. The main results of this paper show that the empirical risk minimizer achieves the optimal performance (up to a logarithmic factor) in a dependent data setting.
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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 | Lecué, G. and Mendelson, S (2016) Performance of empirical risk minimization in linear aggregation | 1.000 | 9 | 5 | 100% |
| 2 | White, H (2001) Asymptotic Theory for Econometricians\/ | 1.000 | 7 | 3 | 100% |
| 3 | Jiang, W. and Tanner, M. A (2010) Risk minimization for time series binary choice with variable selection | 1.000 | 6 | 3 | 100% |
| 4 | Audibert, J.-Y. and Catoni, O (2011) Robust linear least squares regression | 0.737 | 3 | 2 | 100% |
| 5 | Belloni, A., Chernozhukov, V., Chetverikov, D., and Kato, K (2015) Some new asymptotic theory for least squares series: Pointwise and uniform results | 0.737 | 3 | 2 | 100% |
| 6 | Fan, J., Liao, Y., and Mincheva, M (2011) High Dimensional Covariance Matrix Estimation in Approximate Factor Models | 0.737 | 3 | 2 | 100% |
| 7 | Hansen, B. E (2008) Uniform convergence rates for kernel estimation with dependent data | 0.737 | 3 | 2 | 100% |
| 8 | Kock, A. B. and Callot, L (2015) Oracle inequalities for high dimensional vector autoregressions | 0.737 | 3 | 2 | 100% |
| 9 | Newey, W. K (1997) Convergence rates and asymptotic normality for series estimators | 0.737 | 3 | 2 | 100% |
| 10 | Babii, A., Ghysels, E., and Striaukas, J (2021) High-dimensional granger causality tests with an application to vix and news | 0.644 | 2 | 2 | 100% |
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