On inference in high-dimensional regression
On inference in high-dimensional regression
复制标题
高维回归中的推理
DOI：
10.1093/jrsssb/qkad001
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发表时间：
2023
影响因子：
--
通讯作者：
Battey H
中科院分区：
文献类型：
--
作者：
Battey H
本文开发了一种当潜在解释变量的数量大于样本量时在线性回归模型中进行推理的方法。该方法依次将每个回归系数视为兴趣参数，其余系数视为干扰参数，并寻求最佳的兴趣尊重变换，从而在概念费希尔信息矩阵的相关块上引入稀疏性。正如阶乘实验一样，通过对每个变量进行边际最小二乘分析来利用诱导的稀疏性，从而避免惩罚。人们发现问题的一种参数化在计算和数学上都特别方便。特别是，它允许对最优变换问题进行分析解决，从而促进理论分析以及与其他工作的比较。与正则化回归（例如套索及其扩展）相比，不需要调整选择或重新缩放解释变量，从而确保保留回归系数的物理解释。推荐的用法是在更广泛的推理陈述中，以反映模型以及参数的不确定性。简要讨论了将工作扩展到其他回归模型所涉及的考虑因素。
This paper develops an approach to inference in a linear regression model when the number of potential explanatory variables is larger than the sample size. The approach treats each regression coefficient in turn as the interest parameter, the remaining coefficients being nuisance parameters, and seeks an optimal interest-respecting transformation, inducing sparsity on the relevant blocks of the notional Fisher information matrix. The induced sparsity is exploited through a marginal least-squares analysis for each variable, as in a factorial experiment, thereby avoiding penalization. One parameterization of the problem is found to be particularly convenient, both computationally and mathematically. In particular, it permits an analytic solution to the optimal transformation problem, facilitating theoretical analysis and comparison to other work. In contrast to regularized regression, such as the lasso and its extensions, neither adjustment for selection nor rescaling of the explanatory variables is needed, ensuring the physical interpretation of regression coefficients is retained. Recommended usage is within a broader set of inferential statements, so as to reflect uncertainty over the model as well as over the parameters. The considerations involved in extending the work to other regression models are briefly discussed.
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影响因子：
2.7
作者：
D. G. Rasines;G. A. Young
通讯作者：
D. G. Rasines;G. A. Young
影响因子：
2
作者：
Yates, F
通讯作者：
Yates, F
数据模糊：样本分割单个样本
DOI：
--
发表时间：
2021
期刊：
影响因子：
--
作者：
James Leiner Boyan Duan Larry Wasserman Aaditya Ramdas
通讯作者：
James Leiner Boyan Duan Larry Wasserman Aaditya Ramdas
影响因子：
4.5
作者：
Lockhart R;Taylor J;Tibshirani RJ;Tibshirani R
通讯作者：
Tibshirani R
影响因子：
5.7
作者：
Leeb, Hannes;Poetscher, Benedikt M.;Ewald, Karl
通讯作者：
Ewald, Karl