<p>The least absolute shrinkage and selection operator (Lasso) is a popular method for high-dimensional statistics. However, it is known that the Lasso often has estimation bias and prediction error. To address such disadvantages, many alternatives and refitting strategies have been proposed and studied. This work introduces a novel Lasso–Ridge method. Our analysis indicates that the proposed estimator achieves improved prediction performance in a range of settings, including when the Lasso is tuned at the standard theoretical rate. In particular, we derive inequalities that guarantee prediction improvement under mild conditions, thereby clarifying the mechanism through which the proposed method outperforms the Lasso. Moreover, the proposed method retains several key advantages of the Lasso, such as prediction consistency and reliable variable selection. Through extensive numerical studies, including simulations, semi-synthetic experiments, and real data analysis, we further demonstrate that our estimator outperforms the Lasso in both prediction and estimation accuracy, highlighting its potential as a powerful tool for high-dimensional linear regression.</p>

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Lasso–Ridge refitting: a two-stage estimator for high-dimensional linear regression

  • Guo Liu

摘要

The least absolute shrinkage and selection operator (Lasso) is a popular method for high-dimensional statistics. However, it is known that the Lasso often has estimation bias and prediction error. To address such disadvantages, many alternatives and refitting strategies have been proposed and studied. This work introduces a novel Lasso–Ridge method. Our analysis indicates that the proposed estimator achieves improved prediction performance in a range of settings, including when the Lasso is tuned at the standard theoretical rate. In particular, we derive inequalities that guarantee prediction improvement under mild conditions, thereby clarifying the mechanism through which the proposed method outperforms the Lasso. Moreover, the proposed method retains several key advantages of the Lasso, such as prediction consistency and reliable variable selection. Through extensive numerical studies, including simulations, semi-synthetic experiments, and real data analysis, we further demonstrate that our estimator outperforms the Lasso in both prediction and estimation accuracy, highlighting its potential as a powerful tool for high-dimensional linear regression.