Ridge regression revisited: Debiasing, thresholding and bootstrap
重新审视岭回归：去偏、阈值化与自助法AI 解读 ↓
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重新审视岭回归：去偏、阈值化与自助法
- 研究问题
- 高维岭回归如何通过去偏和阈值化缓解偏差并识别稀疏结构，同时支持参数线性组合推断与预测区间构造？
- 方法与思路
- 作者定义去偏阈值化岭估计，证明一致性与高斯近似；用野生自助法进行参数推断，以混合自助法构造预测区间。
- 材料陈述的贡献
- 摘要称，该方法具有相应理论保证，计算可用闭式表达式；模拟显示有限样本表现良好，部分设置下可能更合适。
- 阅读关注点
- 应核对设计矩阵、稀疏性和误差条件，去偏与阈值的选择，以及两种自助法各自针对的推断目标和有效性。
- 阅读边界
- 仅据版本未注明的OpenAlex摘要；定理条件与模拟比较细节未说明，不能将部分设置中的表现概括为普遍优于Lasso。
原文摘要
The success of the Lasso in the era of high-dimensional data can be attributed to its conducting an implicit model selection, that is, zeroing out regression coefficients that are not significant. By contrast, classical ridge regression cannot reveal a potential sparsity of parameters, and may also introduce a large bias under the high-dimensional setting. Nevertheless, recent work on the Lasso involves debiasing and thresholding, the latter in order to further enhance the model selection. As a consequence, ridge regression may be worth another look since—after debiasing and thresholding—it may offer some advantages over the Lasso, for example, it can be easily computed using a closed-form expression. In this paper, we define a debiased and thresholded ridge regression method, and prove a consistency result and a Gaussian approximation theorem. We further introduce a wild bootstrap algorithm to construct confidence regions and perform hypothesis testing for a linear combination of parameters. In addition to estimation, we consider the problem of prediction, and present a novel, hybrid bootstrap algorithm tailored for prediction intervals. Extensive numerical simulations further show that the debiased and thresholded ridge regression has favorable finite sample performance and may be preferable in some settings.