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Performance of Empirical Risk Minimization for Linear Regression with Dependent Data

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  • Christian Brownlees
  • Gu{dh}mundur Stef'an Gu{dh}mundsson

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.

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  • Christian Brownlees & Gu{dh}mundur Stef'an Gu{dh}mundsson, 2021. "Performance of Empirical Risk Minimization for Linear Regression with Dependent Data," Papers 2104.12127, arXiv.org, revised May 2023.
    • Handle: RePEc:arx:papers:2104.12127
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    References listed on IDEAS

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    Cited by:

    1. Toru Kitagawa & Weining Wang & Mengshan Xu, 2022. "Policy Choice in Time Series by Empirical Welfare Maximization," Papers 2205.03970, arXiv.org, revised Jun 2023.

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