Direction identification and minimax estimation in high-dimensional sparse regression via a generalized eigenvalue approach

Sauvenier, Mathieu;Van Bellegem, SΓ©bastien
(2026) Econometric Theory β€” (2026)

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In high-dimensional (HD) sparse linear regression, parameter selection and estimation are addressed using a constraint 𝑙0 on the direction of the parameter vector. We begin by establishing a general result that identifies this direction through the leading generalized eigenspace of specific measurable matrices. Using this result, we propose a novel approach to the selection of the best subsets by solving an empirical generalized eigenvalue problem to estimate the direction of the HD parameter. We then introduce a new estimator based on the RIFLE algorithm, providing a non-asymptotic bound for the estimation risk, minimax convergence, and a central limit theorem. Simulations demonstrate the superiority of our method over existing 𝑙0 -constrained estimators.
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Sauvenier, M., & Van Bellegem, S. (2026). Direction identification and minimax estimation in high-dimensional sparse regression via a generalized eigenvalue approach. Econometric Theory. Accepted/in-press. https://doi.org/10.1017/S0266466626100334 (Original work published 2026)