High-dimensional influence measure
高维影响度量AI 解读 ↓
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高维影响度量
- 研究问题
- 当预测变量数量远超样本量时，如何识别影响后续系数估计、变量选择和筛选的观测，并确定有依据的检测临界值？
- 方法与思路
- 作者构造衡量单个观测对边际相关性影响的高维指标，并在预测变量维度趋于无穷时推导其渐近分布用于检测。
- 材料陈述的贡献
- 摘要称提出了经典 Cook 距离的高维对应度量，建立渐近分布与临界值规则，并用模拟和真实数据展示诊断用途。
- 阅读关注点
- 应核对边际相关性影响的定义、维度与样本量的渐近安排、预测变量依赖条件，以及检测错误率和下游分析的关系。
- 阅读边界
- 仅据版本未注明的 OpenAlex 摘要；渐近条件与检测表现数值未说明，该指标衡量边际相关性影响而非直接衡量系数影响。
原文摘要
Influence diagnosis is important since presence of influential observations could lead to distorted analysis and misleading interpretations. For high-dimensional data, it is particularly so, as the increased dimensionality and complexity may amplify both the chance of an observation being influential, and its potential impact on the analysis. In this article, we propose a novel high-dimensional influence measure for regressions with the number of predictors far exceeding the sample size. Our proposal can be viewed as a high-dimensional counterpart to the classical Cook’s distance. However, whereas the Cook’s distance quantifies the individual observation’s influence on the least squares regression coefficient estimate, our new diagnosis measure captures the influence on the marginal correlations, which in turn exerts serious influence on downstream analysis including coefficient estimation, variable selection and screening. Moreover, we establish the asymptotic distribution of the proposed influence measure by letting the predictor dimension go to infinity. Availability of this asymptotic distribution leads to a principled rule to determine the critical value for influential observation detection. Both simulations and real data analysis demonstrate usefulness of the new influence diagnosis measure.