A smoothing‐based goodness‐of‐fit test of covariance for functional data. Issue 2 (6th April 2019)

• Record Type: Journal Article
• Authors: Chen, Stephanie T.; Xiao, Luo; Staicu, Ana‐Maria
• Is Part Of: Biometrics. Volume 75:Issue 2(2019)
• Page Start: 562
• Page End: 571
• Publication Date: 2019-04-06
• Subjects: functional data analysis -- Functional principal components analysis -- hypothesis testing -- linear mixed effects models -- longitudinal data analysis; Biometry -- Periodicals; 570.15195
• DOI: 10.1111/biom.13005
• Languages: English
• ISSNs: 0006-341X

Abstract

Abstract: Functional data methods are often applied to longitudinal data as they provide a more flexible way to capture dependence across repeated observations. However, there is no formal testing procedure to determine if functional methods are actually necessary. We propose a goodness‐of‐fit test for comparing parametric covariance functions against general nonparametric alternatives for both irregularly observed longitudinal data and densely observed functional data. We consider a smoothing‐based test statistic and approximate its null distribution using a bootstrap procedure. We focus on testing a quadratic polynomial covariance induced by a linear mixed effects model and the method can be used to test any smooth parametric covariance function. Performance and versatility of the proposed test is illustrated through a simulation study and three data applications.