Variable Screening via Quantile Partial Correlation. Issue 518 (3rd April 2017)

• Record Type: Journal Article
• Authors: Ma, Shujie; Li, Runze; Tsai, Chih-Ling
• Is Part Of: Journal of the American Statistical Association. Volume 112:Issue 518(2017)
• Page Start: 650
• Page End: 663
• Publication Date: 2017-04-03
• Subjects: Quantile correlation -- Quantile partial correlation -- Screening -- Variable selection; Statistics -- Periodicals; Statistics -- Periodicals; Statistiques -- Périodiques; États-Unis -- Statistiques -- Périodiques; 519.5
• DOI: 10.1080/01621459.2016.1156545
• Languages: English
• ISSNs: 0162-1459

Abstract

ABSTRACT: In quantile linear regression with ultrahigh-dimensional data, we propose an algorithm for screening all candidate variables and subsequently selecting relevant predictors. Specifically, we first employ quantile partial correlation for screening, and then we apply the extended Bayesian information criterion (EBIC) for best subset selection. Our proposed method can successfully select predictors when the variables are highly correlated, and it can also identify variables that make a contribution to the conditional quantiles but are marginally uncorrelated or weakly correlated with the response. Theoretical results show that the proposed algorithm can yield the sure screening set. By controlling the false selection rate, model selection consistency can be achieved theoretically. In practice, we proposed using EBIC for best subset selection so that the resulting model is screening consistent. Simulation studies demonstrate that the proposed algorithm performs well, and an empirical example is presented. Supplementary materials for this article are available online.