报告题目：Model-Free Feature Screening for Ultrahigh Dimensional Data through a Modified Blum-Kiefer-Rosenblatt Correlation 报 告 人：朱利平教授（中国人民大学统计与大数据研究院） 报告时间：4月28日（周4）上午10：00-11：00 报告地点：知新楼B-1238室 摘 要：In this paper we introduce a modified Blum-Kiefer-Rosenblatt correlation (MBKR for short) to rank the relative importance of each predictor in ultrahigh dimensional regressions. We advocate using the MBKR for two reasons. First, the MBKR is nonnegative and equals zero if and only if two random variables are independent, indicating that the MBKR can detect nonlinear dependence. We illustrate that the sure independence screening procedure based on the MBKR (MBKR-SIS for short) is effective to detect nonlinear effects including interactions and heterogeneity, particularly when both continuous and discrete predictors are involved simultaneously. Second, the MBKR is conceptually simple, easy to implement and affine-invariant. The MBKR is free of tuning parameters and no iteration is required in estimation. It remains unchanged when order-preserving transformations are applied to the response or predictors, indicating that the MBKR-SIS is robust to the presence of extreme values and outliers in the observations. We also show that, under mild conditions, the MBKR-SIS procedure has the desirable sure screening and ranking consistency properties, which guarantee that all important predictors can be retained after screening with probability approaching one. We demonstrate the merits of the MBKR-SIS procedure through simulations and an application to a real-world dataset. 朱利平教授介绍 2006年于华东师范大学取得博士学位。现任中国人民大学统计与大数据研究院教授、博士生导师。 朱利平博士一直从事统计理论、方法与应用研究，研究兴趣涉及半参数建模、高维数据分析、充分降维以及变量选择等领域。在Journal of American Statistical Association, Journal of the Royal Statistical Society Series B, Annals of Statistics以及Biometrika等统计学国际重要学术期刊发表论文60余篇。 欢迎各位老师同学积极参加！ |
