$\ell_1$-Regularized Generalized Least Squares

• URL: http://arxiv.org/abs/2405.10719v1
• Date: Fri, 17 May 2024 12:03:24 GMT
• Title: $\ell_1$-Regularized Generalized Least Squares
• Authors: Kaveh S. Nobari, Alex Gibberd,
• Abstract summary: We establish non-asymptotic oracle inequalities for estimation accuracy in a framework that allows for persistent autoregressive errors. A simulation study verifies the performance of the proposed method, demonstrating that the penalized (feasible) GLS-LASSO estimator performs on par with the LASSO in the case of white noise errors.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper we propose an $\ell_1$-regularized GLS estimator for high-dimensional regressions with potentially autocorrelated errors. We establish non-asymptotic oracle inequalities for estimation accuracy in a framework that allows for highly persistent autoregressive errors. In practice, the Whitening matrix required to implement the GLS is unkown, we present a feasible estimator for this matrix, derive consistency results and ultimately show how our proposed feasible GLS can recover closely the optimal performance (as if the errors were a white noise) of the LASSO. A simulation study verifies the performance of the proposed method, demonstrating that the penalized (feasible) GLS-LASSO estimator performs on par with the LASSO in the case of white noise errors, whilst outperforming it in terms of sign-recovery and estimation error when the errors exhibit significant correlation.

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