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Performance of Empirical Risk Minimization for Linear Regression with Dependent Data

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

Abstract

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.

Citation extraction

47
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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
1Lecué, G. and Mendelson, S (2016) Performance of empirical risk minimization in linear aggregation1.00095100%
2White, H (2001) Asymptotic Theory for Econometricians\/1.00073100%
3Jiang, W. and Tanner, M. A (2010) Risk minimization for time series binary choice with variable selection1.00063100%
4Audibert, J.-Y. and Catoni, O (2011) Robust linear least squares regression0.73732100%
5Belloni, A., Chernozhukov, V., Chetverikov, D., and Kato, K (2015) Some new asymptotic theory for least squares series: Pointwise and uniform results0.73732100%
6Fan, J., Liao, Y., and Mincheva, M (2011) High Dimensional Covariance Matrix Estimation in Approximate Factor Models0.73732100%
7Hansen, B. E (2008) Uniform convergence rates for kernel estimation with dependent data0.73732100%
8Kock, A. B. and Callot, L (2015) Oracle inequalities for high dimensional vector autoregressions0.73732100%
9Newey, W. K (1997) Convergence rates and asymptotic normality for series estimators0.73732100%
10Babii, A., Ghysels, E., and Striaukas, J (2021) High-dimensional granger causality tests with an application to vix and news0.64422100%

Showing the top 10 of 47 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Performance of Empirical Risk Minimization For Principal Component Regression0.95074
2Concentration Inequalities for Suprema of Empirical Processes with Dependent Data via Generic Chaining with Applications to Statistical Learning0.92843