Estimating Truncated Functional Linear Models With a Nested Group Bridge Approach. Issue 3 (2nd July 2020)

• Record Type: Journal Article
• Authors: Guan, Tianyu; Lin, Zhenhua; Cao, Jiguo
• Is Part Of: Journal of computational and graphical statistics. Volume 29:Issue 3(2020)
• Page Start: 620
• Page End: 628
• Publication Date: 2020-07-02
• Subjects: B-spline basis functions -- Functional data analysis -- Functional linear regression -- Group bridge approach -- Locally sparse -- Penalized B-splines; Mathematical statistics -- Data processing -- Periodicals; Mathematical statistics -- Graphic methods -- Periodicals; 519.50285
• DOI: 10.1080/10618600.2020.1713797
• Languages: English
• ISSNs: 1061-8600

Abstract

Abstract: We study a scalar-on-function truncated linear regression model which assumes that the functional predictor does not influence the response when the time passes a certain cutoff point. We approach this problem from the perspective of locally sparse modeling, where a function is locally sparse if it is zero on a substantial portion of its defining domain. In the truncated linear model, the slope function is exactly a locally sparse function that is zero beyond the cutoff time. A locally sparse estimate then gives rise to an estimate of the cutoff time. We propose a nested group bridge penalty that is able to specifically shrink the tail of a function. Combined with the B-spline basis expansion and penalized least squares, the nested group bridge approach can identify the cutoff time and produce a smooth estimate of the slope function simultaneously. The proposed nested group bridge estimator is shown to be consistent, while its numerical performance is illustrated by simulation studies. The proposed nested group bridge method is demonstrated with an application of determining the effect of the past engine acceleration on the current particulate matter emission. Supplementary materials for this article are available online.