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

Mathieu Sauvenier () and Sébastien Van Bellegem ()
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Mathieu Sauvenier: Université catholique de Louvain, LIDAM/CORE, Belgium
Sébastien Van Bellegem: Université catholique de Louvain, LIDAM/CORE, Belgium

No 3351, LIDAM Reprints CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: 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.

Pages: 39
Date: 2026-03-03
Note: In: Econometric Theory, 2026
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Persistent link: https://EconPapers.repec.org/RePEc:cor:louvrp:3351

DOI: 10.1017/S0266466626100334

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