Performance of Empirical Risk Minimization for Linear Regression with Dependent Data
38 Pages Posted: 21 Apr 2021 Last revised: 14 May 2021
Date Written: April 20, 2021
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
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