Speaker: Zhu Liping, Professor, Institute of Statistics and Big Data, Renmin University of China
Date: April 28, 2016
Time: 10:00am - 11:00 am
Location: Room B1238, Zhixin Building, Central Campus
Sponsor: Qilu Securities Institute for Financial Studies
In this paper we introduce a modified Blum-Kiefer-Rosenblatt correlation (MBKR for short) to rank the relative importance o 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.
Prof. Zhu Liping completed his Doctor’s Degree in East China Normal University in 2006. He is currently a professor and doctoral supervisor of Institute of Statistics and Big Data, Renmin University of China. He was selected in Program for New Century Excellent Talents of Minister of Education and Program for Young Talents of the Organization Department of the Central Committee of the CPC. He was funded by Program of Outstanding Young of National Natural Science Foundation of China. Pro. Zhu engages in statistical theory, methods and application fields. And his research includes half-parameterized modeling, high dimensional data analysis, full dimensional reduction and variable selection etc. Pro. Zhu has published more than 60 papers in international important scientific journals such as Journal of American Statistical Association, Journal of the Royal Statistical Society Series B, Annals of Statistics and Biometrika.
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Edited by: Liu Huan