Composite Coefficient of Determination and Its Application in Ultrahigh Dimensional Variable Screening

• 成果类型: Article
• 署名作者: Kong, Efang; Xia, Yingcun; Zhong, Wei
• 署名单位: University of Electronic Science & Technology of China; National University of Singapore; Xiamen University; Xiamen University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2018.1514305
• 发表日期: 2019
• 页码: 1740-1751
• 关键词: INDEPENDENCE; selection; alox12; gene; association; dependence; landscape; models; cancer

摘要

In this article, we propose to measure the dependence between two random variables through a composite coefficient of determination (CCD) of a set of nonparametric regressions. These regressions take consecutive binarizations of one variable as the response and the other variable as the predictor. The resulting measure is invariant to monotonic marginal variable transformation, rendering it robust against heavy-tailed distributions and outliers, and convenient for independent testing. Estimation of CCD could be done through kernel smoothing, with a consistency rate of root-n. CCD is a natural measure of the importance of variables in regression and its sure screening property, when used for variable screening, is also established. Comprehensive simulation studies and real data analysis show that the newly proposed measure quite often turns out to be the most preferred compared to other existing methods both in independence testing and in variable screening. for this article are available online.