Performance of Empirical Risk Minimization For Principal Component Regression

Christian Brownlees, Gu{\dh}mundur Stef\'an Gu{\dh}mundsson and Yaping Wang

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Abstract: This paper studies the predictive performance of empirical risk minimization for principal component regression. Our analysis accommodates the leading eigenvalues of the predictor covariance matrix growing either linearly or sublinearly with the number of predictors. Additionally, we allow for both light-tailed and heavy-tailed data. Our main result establishes that, under appropriate conditions, empirical risk minimization for principal component regression is consistent for prediction and achieves near-optimal performance.

Date: 2024-09, Revised 2026-07
New Economics Papers: this item is included in nep-ecm and nep-ipr
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