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DIRECTION IDENTIFICATION AND MINIMAX ESTIMATION IN HIGH-DIMENSIONAL SPARSE REGRESSION VIA A GENERALIZED EIGENVALUE APPROACH

Mathieu Sauvenier & Sébastien Van Bellegem

Econometric Theory2026https://doi.org/10.1017/s0266466626100334article
AJG 4ABDC A*
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0.50

Abstract

In high-dimensional (HD) sparse linear regression, parameter selection and estimation are addressed using a constraint $l_0$ 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 $l_0$ -constrained estimators.

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https://doi.org/https://doi.org/10.1017/s0266466626100334

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@article{mathieu2026,
  title        = {{DIRECTION IDENTIFICATION AND MINIMAX ESTIMATION IN HIGH-DIMENSIONAL SPARSE REGRESSION VIA A GENERALIZED EIGENVALUE APPROACH}},
  author       = {Mathieu Sauvenier & Sébastien Van Bellegem},
  journal      = {Econometric Theory},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1017/s0266466626100334},
}

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F · citation impact0.50 × 0.4 = 0.20
M · momentum0.50 × 0.15 = 0.07
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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