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中国人民大学朱利平教授: Test effects of high-dimensional covariates via aggregating cumulative covariances

光华讲坛——社会名流与企业家论坛第 6171 期

Test effects of high-dimensional covariates via aggregating cumulative covariances

主讲人中国人民大学朱利平教授

主持人统计学院林华珍教授

时间2022614日(周二)上午10:30-11:30

直播平台及会议ID:腾讯会议,ID: 547-309-864

主办单位:统计研究中心和统计学院 科研处

主讲人简介:

朱利平,中国人民大学“杰出学者”特聘教授,统计与大数据研究院副院长、博士生导师,国家高层次人才计划入选者。朱利平一直从事复杂高维数据、超高维数据、非线性相依数据分析方法和理论研究,多篇论文入选高被引论文。现任中国现场统计学会高维数据分会副理事长、生存分析分会副理事长等,先后受邀担任国际统计学领域顶级学术期刊《The Annals of Statistics》、《Statistica Sinica》、《Journal of Multivariate Analysis》等期刊编委。

内容提要:

In this talk, we test for the effects of high-dimensional covariates on the response. In many applications, different components of covariates usually exhibit various levels of variation, which is ubiquitous in high-dimensional data. To simultaneously accommodate such heteroscedasticity and high dimensionality, we propose a novel test based on an aggregation of the marginal cumulative covariances, requiring no prior information on the specific form of regression models. Our proposed test statistic is scale-invariance, tuning-free and convenient to implement. The asymptotic normality of the proposed statistic is established under the null hypothesis. We further study the asymptotic relative efficiency of our proposed test with respect to the state-of-art universal tests in two different settings: one is designed for high-dimensional linear model and the other is introduced in a completely model-free setting. A remarkable finding reveals that, thanks to the scale-invariance property, even under the high-dimensional linear models, our proposed test is asymptotically much more powerful than existing competitors for the covariates with heterogeneous variances while maintaining high efficiency for the homoscedastic ones.

在本次演讲中,我们测试了高维协变量对响应的影响。在许多应用中,协变量的不同分量通常表现出不同程度的变化,这在高维数据中无处不在。为了同时适应这种异方差性和高维性,我们提出了一种基于边际累积协方差聚合的新测试,不需要关于特定形式的回归模型的先验信息。我们提出的测试统计量是尺度不变的,无需调整且易于实现。所提出的统计量的渐近正态性是在原假设下建立的。我们进一步研究了我们提出的测试在两种不同设置中相对于最先进的通用测试的渐近相对效率:一种是为高维线性模型设计的,另一种是在完全无模型的设置中引入的。一个显着的发现表明,由于尺度不变性,即使在高维线性模型下,我们提出的测试在具有异质方差的协变量上也比现有的竞争者渐近地强大得多,同时对同方差的协变量保持高效率。


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