講座主題：Test the effects of  high-dimensionalcovariates via aggregating cumulative covariances

報告人🌂：朱利平（中國人民大學統計與大數據研究院院長🧔🏻，國家傑青）

時間：2022年9月22日上午09：00-11：00

線上會議🫱🏻🧗🏻：騰訊會議號920-582-024

報告人簡介：朱利平，中國人民大學“傑出學者”特聘教授🧑🏼‍🍼🎒、博士生導師👩‍🚀，統計與大數據研究院院長，國家重大人才工程入選者，國家傑出青年基金獲得者。

朱利平教授長期從事復雜數據分析方法和理論研究工作，在復雜高維、超高維數據領域以及非線性相依數據領域做出了一系列有影響力的研究工作。多篇論文入選ESI高被引論文。現任中國現場統計學會高維數據分會和生存分析分會副理事長，以及多個學會的常務理事、理事等🦹🏿‍♀️。先後擔任統計學領域國際頂級學術期刊《The Annals of Statistics》、國際重要學術期刊《StatisticaSinica》和《Journal of Multivariate Analysis》等國際學術期刊AssociateEditor🚼，以及《系統科學與數學》和《應用概率統計》等國內重要學術期刊編委。

內容摘要：In this talk I shall introduce how to test for the  effects of high-dimensional covariates on theresponse.  In many applications,different components of covariates usually exhibit various levels of variation,which is ubiquitous in high-dimensional data. To simultaneously accommodatesuch heteroscedasticity and high dimensionality, we propose a novel test basedon an aggregation of the marginal cumulative covariances,  requiring no prior information on the specificform of regression models. Our proposed test statistic is scale-invariant,tuning-free and convenient to implement. The asymptotic normality of the proposed statistic is established underthe  null hypothesis. We further studythe asymptotic relative efficiency of our proposed test with respect to thestate-of-art universal tests in two different settings: one is designed forhigh-dimensional linear model and the other is introduced in a completelymodel-free setting. A remarkable finding reveals that, thanks to the scale-invariantproperty, even under the high-dimensional linear models, our proposed test isasymptotically much more powerful than existing competitors for the covariateswith heterogeneous variances while maintaining high efficiency for thehomoscedastic ones.