Skip to main content
Article
Tensor product splines and functional principal components
Journal of Statistical Planning and Inference (2020)
  • Prof. Philip T. Reiss
  • Meng Xu
Abstract
Functional principal component analysis for sparse longitudinal data usually proceeds by first smoothing the covariance surface, and then obtaining an eigendecomposition of the associated covariance operator. Here we consider the use of penalized tensor product splines for the initial smoothing step. Drawing on a result regarding finite-rank symmetric integral operators, we derive an explicit spline representation of the estimated eigenfunctions, and show that the effect of penalization can be notably disparate for alternative approaches to tensor product smoothing. The latter phenomenon is illustrated with two data sets derived from magnetic resonance imaging of the human brain.
Keywords
  • bivariate smoothing,
  • covariance function,
  • covariance operator,
  • eigenfunction,
  • roughness penalty
Publication Date
2020
Citation Information
Philip T. Reiss and Meng Xu. "Tensor product splines and functional principal components" Journal of Statistical Planning and Inference (2020)
Available at: http://works.bepress.com/phil_reiss/46/