Performance of empirical risk minimization for linear regression with dependent data

Brownlees, Christian, 1979-; Gudmundsson, Gudmundur Stefan

doi:http://dx.doi.org/10.1017/S0266466623000348

Performance of empirical risk minimization for linear regression with dependent data

Citation

Brownlees C, Guđmundsson GS. Performance of empirical risk minimization for linear regression with dependent data. Econ Theory. 2023. 30 p. DOI: 10.1017/S0266466623000348

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.