Performance of Empirical Risk Minimization for Linear Regression with Dependent Data

38 Pages Posted: 21 Apr 2021 Last revised: 14 May 2021

See all articles by Christian T. Brownlees

Christian T. Brownlees

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences; Barcelona Graduate School of Economics (Barcelona GSE)

Gudmundur Gudmundsson

Aarhus BSS; Aarhus University - CREATES

Date Written: April 20, 2021

Abstract

This paper establishes oracle inequalities for the prediction risk of the empirical risk minimizer 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 assumed to be unknown. The main results of this paper indicate 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://84.89.132.1/~cbrownlees/

Barcelona Graduate School of Economics (Barcelona GSE) ( email )

Ramon Trias Fargas 25-27
Barcelona, Catalonia 08014
Spain

Gudmundur Gudmundsson

Aarhus BSS ( email )

Fuglesangs Allé 4
Aarhus V, 8210
Denmark

Aarhus University - CREATES ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
38
Abstract Views
123
PlumX Metrics