Group screening for ultra-high-dimensional feature under linear model

Abstract

Ultra-high-dimensional data with grouping structures arise naturally in many contemporary statistical problems, such as gene-wide association studies and the multi-factor analysis-of-variance (ANOVA). To address this issue, we proposed a group screening method to do variables selection on groups of variables in linear models. This group screening method is based on a working independence, and sure screening property is also established for our approach. To enhance the finite sample performance, a data-driven thresholding and a two-stage iterative procedure are developed. To the best of our knowledge, screening for grouped variables rarely appeared in the literature, and this method can be regarded as an important and non-trivial extension of screening for individual variables. An extensive simulation study and a real data analysis demonstrate its finite sample performance.

Keywords:

• Ultra-high-dimensional
• group screening
• linear model
• sure screening property

AMS 2000 Subject Classifications:

• 62G05
• 62E20

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the National Natural Science Foundation of China (CN) (11571112), the National Social Science Foundation Key Program (17ZDA091) and Natural Science Fund of Education Department of Anhui Province (KJ2013B233), the 111 Project of China (B14019).

Notes on contributors

Yong Niu

Yong Niu is a PhD candidate in the College of Statistics, East China Normal University, Shanghai, China. His research interests include high dimensional data, big data analytics and nonparametric statistics.

Riquan Zhang

Riquan Zhang is a professor and chair of School of Statistics in East China Normal University. His research interests include high dimensional data, big data analytics, functional data analysis, statistical machine learning and nonparametric statistics.

Jicai Liu

Jicai Liu is an associate professor of statistics in the department of mathematics at Shanghai Normal University, China. His research interests include high dimensional data, lifetime data analysis and nonparametric statistics.

Huapeng Li

Huapeng Li is an associate professor of statistics in the school of mathematics and statistics at Datong University, China. His research interests include nonparametric and semiparametric statistics based on empirical likelihood, selection biased data and finite mixture models.