Random weighting in LASSO regression
| Autor: | Ng, Tun Lee, Newton, Michael A. |
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| Rok vydání: | 2020 |
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| Zdroj: | Electron. J. Statist. 16 (2022) 3430-3481 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1214/22-EJS2020 |
| Popis: | We establish statistical properties of random-weighting methods in LASSO regression under different regularization parameters $\lambda_n$ and suitable regularity conditions. The random-weighting methods in view concern repeated optimization of a randomized objective function, motivated by the need for computational approximations to Bayesian posterior sampling. In the context of LASSO regression, we repeatedly assign analyst-drawn random weights to terms in the objective function (including the penalty terms), and optimize to obtain a sample of random-weighting estimators. We show that existing approaches have conditional model selection consistency and conditional asymptotic normality at different growth rates of $\lambda_n$ as $n \to \infty$. We propose an extension to the available random-weighting methods and establish that the resulting samples attain conditional sparse normality and conditional consistency in a growing-dimension setting. We find that random-weighting has both approximate-Bayesian and sampling-theory interpretations. Finally, we illustrate the proposed methodology via extensive simulation studies and a benchmark data example. Comment: Update data presentation |
| Databáze: | arXiv |
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