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ridge regressioninferencehigh-dimensional

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Optimal Bias-Correction and Valid Inference in High-Dimensional Ridge Regression: A Closed-Form Solution

Zhaoxing Gao · Ruey S. Tsay首次提交 2024-05-01 · 修订 2024-07-24 · v2arXiv预印本

高维岭回归中的最优偏差修正与有效推断：闭式解AI 解读 ↓

正则化与变量选择

关联记录被引 0 次 ↗OpenAlex · 核验 2026-09-30

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arXiv

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arXiv：2405.00424 · v2

首次提交：2024-05-01 · 最近修订：2024-07-24

原站分类：econ.EM / stat.ME / stat.ML

收录依据：arXiv 计量经济学分类（econ.EM）

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代码、数据与补充材料

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关注这篇论文的作者

Zhaoxing Gao

Ruey S. Tsay

AI 解读 · 基于可核验材料

高维岭回归中的最优偏差修正与有效推断：闭式解

研究问题: 如何修正岭回归在维数低于或高于样本量时的偏差，并在维数、样本量及迭代次数增长时开展有效推断？
方法与思路: 作者提出迭代偏差修正；维数超过样本量时先考察线性变换可消除的偏差，再以岭筛选形成适于修正的缩减模型。
材料陈述的贡献: 摘要称方法刻画了线性变换的偏差修正极限，给出筛选模型包含真实模型的条件，并建立渐近性质与推断结果。
阅读关注点: 应核对剩余偏差的最优性定义、筛选包含真实模型的条件，以及迭代次数、维数和样本量的联合增长要求。
阅读边界: 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要的维数比较公式存在缺损，且未列明有效推断的具体条件。

GPT-6.1 Sol · 高 · 2026-10-03

原文摘要

Ridge regression is an indispensable tool in big data analysis. Yet its inherent bias poses a significant and longstanding challenge, compromising both statistical efficiency and scalability across various applications. To tackle this critical issue, we introduce an iterative strategy to correct bias effectively when the dimension $p$ is less than the sample size $n$ . For $p>n$ , our method optimally mitigates the bias such that any remaining bias in the proposed de-biased estimator is unattainable through linear transformations of the response data. To address the remaining bias when $p>n$ , we employ a Ridge-Screening (RS) method, producing a reduced model suitable for bias correction. Crucially, under certain conditions, the true model is nested within our selected one, highlighting RS as a novel variable selection approach. Through rigorous analysis, we establish the asymptotic properties and valid inferences of our de-biased ridge estimators for both $p n$ , where, both $p$ and $n$ may increase towards infinity, along with the number of iterations. We further validate these results using simulated and real-world data examples. Our method offers a transformative solution to the bias challenge in ridge regression inferences across various disciplines.Ridge regression is an indispensable tool in big data analysis. Yet its inherent bias poses a significant and longstanding challenge, compromising both statistical efficiency and scalability across various applications. To tackle this critical issue, we introduce an iterative strategy to correct bias effectively when the dimension $p$ is less than the sample size $n$. For $p>n$, our method optimally mitigates the bias such that any remaining bias in the proposed de-biased estimator is unattainable through linear transformations of the response data. To address the remaining bias when $p>n$, we employ a Ridge-Screening (RS) method, producing a reduced model suitable for bias correction. Crucially, under certain conditions, the true model is nested within our selected one, highlighting RS as a novel variable selection approach. Through rigorous analysis, we establish the asymptotic properties and valid inferences of our de-biased ridge estimators for both $p n$, where, both $p$ and $n$ may increase towards infinity, along with the number of iterations. We further validate these results using simulated and real-world data examples. Our method offers a transformative solution to the bias challenge in ridge regression inferences across various disciplines.

摘要来源：arXiv

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