Nonparametric Screening for Additive Quantile Regression in Ultra-high Dimension

Speaker:  Daoji Li, California State University, Fullerton.

Time:       4:00 pm, Aug. 21^st

Location: SIST2 415

Host:        Qifeng Liao

Abstract:

In practical applications, one often does not know the true structure of the underlying conditional quantile function, especially in the ultra-high dimensional setting. To deal with ultra-high dimensionality, quantile-adaptive marginal nonparametric screening methods have been recently developed. However, these approaches may miss important covariates that are marginally independent of the response or may select unimportant covariates due to their high correlations with important covariates. To mitigate such shortcomings, we develop a conditional nonparametric quantile screening procedure (complemented by subsequent selection) for nonparametric additive quantile regression models. Under some mild conditions, we show that the proposed screening method can identify all relevant covariates in a small number of steps with probability approaching one. The subsequent narrowed best subset (via a modified Bayesian information criterion) also contains all the relevant covariates with overwhelming probability. The advantages of our proposed procedure are demonstrated through simulation studies and a real data example. This is a joint work with Yinfei Kong and Dawit Zerom.

Bio:

Dr. Daoji Li is Associate Professor of Data Science and Statistics in College of Business and Economics at California State University, Fullerton (CSUF).  Before joining CSUF, he was Assistant Professor in the Department of Statistics and Data Science at University of Central Florida. Prior to that, He was Postdoctoral Research Associate in the Data Sciences and Operations Department of the Marshall School of Business at the University of Southern California. He received his Ph.D. in Statistics from the University of Manchester, United Kingdom. His research interests include feature screening, deep learning, causal inference, high dimensional statistics, and longitudinal data analysis.  His papers have been published in top journals in statistics and business, including the Annals of Statistics, Journal of Business & Economic Statistics, and Journal of Business Research.