A smoothing-based goodness-of-fit test of covariance for functional data

Biometrics. 2019 Jun;75(2):562-571. doi: 10.1111/biom.13005. Epub 2019 Apr 6.


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.

Keywords: Functional principal components analysis; functional data analysis; hypothesis testing; linear mixed effects models; longitudinal data analysis.

Publication types

  • Research Support, N.I.H., Extramural
  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Analysis of Variance
  • Computer Simulation
  • Data Interpretation, Statistical*
  • Humans
  • Longitudinal Studies
  • Models, Statistical*