Performance of Empirical Risk Minimization for Linear Regression with Dependent Data

38 Pages Posted: 21 Apr 2021 Last revised: 30 May 2023

See all articles by Christian T. Brownlees

Christian T. Brownlees

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences

Gudmundur Gudmundsson

Aarhus BSS

Date Written: April 20, 2021

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.

Keywords: empirical risk minimization, linear regression, time series, oracle inequality

JEL Classification: C13, C14, C22, C55

Suggested Citation

Brownlees, Christian T. and Gudmundsson, Gudmundur, Performance of Empirical Risk Minimization for Linear Regression with Dependent Data (April 20, 2021). Available at SSRN: https://ssrn.com/abstract=3830639 or http://dx.doi.org/10.2139/ssrn.3830639

Christian T. Brownlees (Contact Author)

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences ( email )

Ramon Trias Fargas 25-27
Barcelona, 08005
Spain

HOME PAGE: http://econ.upf.edu/~cbrownlees/

Gudmundur Gudmundsson

Aarhus BSS ( email )

Fuglesangs Allé 4
Aarhus V, 8210
Denmark

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