Performance of Empirical Risk Minimization for Linear Regression with Dependent Data

Christian Brownlees and Gu{\dh}mundur Stef\'an Gu{\dh}mundsson
Authors registered in the RePEc Author Service: Guðmundur Stefán Guðmundsson

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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.

Date: 2021-04, Revised 2023-05
New Economics Papers: this item is included in nep-ecm and nep-rmg
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2104.12127

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