High Dimensional Influence Measure
High Dimensional Influence Measure
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DOI：
10.2139/ssrn.2317649
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发表时间：
2013-08
期刊：
影响因子：
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通讯作者：
Junlong Zhao;Chenlei Leng;Lexin Li;Hansheng Wang
中科院分区：
文献类型：
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作者：
Junlong Zhao;Chenlei Leng;Lexin Li;Hansheng Wang
影响诊断很重要，因为有影响的观察结果的存在可能导致扭曲的分析和误导性的解释。对于高维数据，尤其如此，因为增加的维度和复杂性可能会放大观察结果具有影响力的机会及其对分析的潜在影响。在这篇文章中，我们提出了一个新的高维影响措施的回归预测的数量远远超过样本量。我们的建议可以被看作是一个高维对应的经典库克距离。然而，尽管库克距离量化了个体观测对最小二乘回归系数估计的影响，但我们的新诊断措施捕获了对边际相关性的影响，这反过来又对下游分析产生了严重影响，包括系数估计，变量选择和筛选。此外，我们建立了渐近分布的影响措施，让预测维度走向无穷大。这种渐近分布的可用性导致一个原则性的规则，以确定有影响力的观察检测的临界值。仿真和真实的数据分析都证明了新的影响诊断措施的实用性。
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.