Estimating the error variance in a high-dimensional linear model
高维线性模型中的误差方差估计AI 解读 ↓
← 返回论文列表与筛选
阅读说明
本页整理公开书目信息，不生成学术质量评分。AI 解读根据题名及所注明的摘要或原文片段生成，未完成全文核验，可能有误；具体假设、证明与结论请核对原文。摘要保留来源文本，未经模型改写。
DOI 首次登记不等于接收或发表日期。部分更正、评论等条目没有独立摘要；缺少可靠材料时保留待补状态。
引用量采用 OpenAlex 单条关联记录，不合计多个记录；关联记录可能包含正式发表版本，不等于此版本单独引用。缺失不视为零，引用指标不代表论文质量。
关注作者按书目中的完整姓名匹配，同名和姓名变体需人工辨别。相关论文先按共享细分方向和具体方法排列，再参考通用方法与发表日期。
分类依据与纠错
AI 根据所提供的论文材料归类：摘要研究高维线性模型误差方差的通用估计问题，未涉及所列经济学细分方向所需的具体模型或应用证据。
反馈分类问题
正在核对关联版本…
代码、数据与补充材料
正在核对对应版本的资源…
关注这篇论文的作者
高维线性模型中的误差方差估计
- 研究问题
- 在高维线性回归中，尤其真实非零系数集合难以恢复时，如何估计误差方差并控制估计的均方误差？
- 方法与思路
- 作者利用高斯分布的自然参数化构造惩罚似然，提出 natural lasso，并另提出理论上无需调节正则化参数的 organic lasso。
- 材料陈述的贡献
- 摘要称，natural lasso 的均方误差理论结果不要求对设计矩阵或真实系数作假设，并拓宽了已有方法的适用条件。
- 阅读关注点
- 应核对误差界对信号、样本量和正则化参数的依赖，以及 organic lasso 无需调参的准确含义和实证实施方式。
- 阅读边界
- 仅据 Crossref 摘要；无设计或系数假设不等于没有分布等其他条件，具体误差界、参数选择与比较数值未提供。
原文摘要
Summary The lasso has been studied extensively as a tool for estimating the coefficient vector in the high-dimensional linear model; however, considerably less is known about estimating the error variance in this context. In this paper, we propose the natural lasso estimator for the error variance, which maximizes a penalized likelihood objective. A key aspect of the natural lasso is that the likelihood is expressed in terms of the natural parameterization of the multi-parameter exponential family of a Gaussian with unknown mean and variance. The result is a remarkably simple estimator of the error variance with provably good performance in terms of mean squared error. These theoretical results do not require placing any assumptions on the design matrix or the true regression coefficients. We also propose a companion estimator, called the organic lasso, which theoretically does not require tuning of the regularization parameter. Both estimators do well empirically compared to pre-existing methods, especially in settings where successful recovery of the true support of the coefficient vector is hard. Finally, we show that existing methods can do well under fewer assumptions than previously known, thus providing a fuller story about the problem of estimating the error variance in high-dimensional linear models.