Variance estimation in high-dimensional linear models
高维线性模型中的方差估计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：摘要研究通用高维线性模型的总体量估计，残差方差和解释比例不构成金融波动率或因子模型的分类依据。
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
高维线性模型中的方差估计
- 研究问题
- 当预测变量数接近甚至超过样本量，且信号不满足稀疏性时，能否仍一致估计残差方差、解释变异比例和信号强度？
- 方法与思路
- 作者提出基于矩方法的估计量，在高斯预测变量和误差的高维线性模型中研究一致性及渐近正态性，并以数值和真实数据评估。
- 材料陈述的贡献
- 摘要称无需信号稀疏假设即可估计相关总体量，一致性还涵盖维数与样本量之比趋于无穷的情形，即使信号本身无法估计。
- 阅读关注点
- 应核对预测变量协方差与信号规模的条件、不同维数增长情形的结论范围，以及高斯假设放宽究竟有理论还是仅数值支持。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；完整条件未说明，极高维情形明确陈述的是一致性，不能自动扩展其渐近正态结论。
原文摘要
The residual variance and the proportion of explained variation are important quantities in many statistical models and model fitting procedures. They play an important role in regression diagnostics and model selection procedures, as well as in determining the performance limits in many problems. In this paper we propose new method-of-moments-based estimators for the residual variance, the proportion of explained variation and other related quantities, such as the ℓ2 signal strength. The proposed estimators are consistent and asymptotically normal in high-dimensional linear models with Gaussian predictors and errors, where the number of predictors d is proportional to the number of observations n; in fact, consistency holds even in settings where d/n → ∞. Existing results on residual variance estimation in high-dimensional linear models depend on sparsity in the underlying signal. Our results require no sparsity assumptions and imply that the residual variance and the proportion of explained variation can be consistently estimated even when d>n and the underlying signal itself is nonestimable. Numerical work suggests that some of our distributional assumptions may be relaxed. A real-data analysis involving gene expression data and single nucleotide polymorphism data illustrates the performance of the proposed methods.