title: Modeling functional data with spatially heterogeneous shape characteristics.
abstract: We propose a novel class of models for functional data exhibiting skewness or other shape characteristics that vary with spatial or temporal location. We use copulas so that the marginal distributions and the dependence structure can be modeled independently. Dependence is modeled with a Gaussian or t-copula, so that there is an underlying latent Gaussian process. We model the marginal distributions using the skew t family. The mean, variance, and shape parameters are modeled nonparametrically as functions of location. A computationally tractable inferential framework for estimating heterogeneous asymmetric or heavy-tailed marginal distributions is introduced. This framework provides a new set of tools for increasingly complex data collected in medical and public health studies. Our methods were motivated by and are illustrated with a state-of-the-art study of neuronal tracts in multiple sclerosis patients and healthy controls. Using the tools we have developed, we were able to find those locations along the tract most affected by the disease. However, our methods are general and highly relevant to many functional data sets. In addition to the application to one-dimensional tract profiles illustrated here, higher-dimensional extensions of the methodology could have direct applications to other biological data including functional and structural magnetic resonance imaging (MRI).
authors: Department of Statistics, North Carolina State University, 2311 Stinson Drive, Campus Box 8203, Raleigh, North Carolina 27695-8203, USA. ana-maria staicu@ncsu.edu
authors: Ana-Maria
authors: AM
authors: Staicu
authors: Ciprian M
authors: CM
authors: Crainiceanu
authors: Daniel S
authors: DS
authors: Reich
authors: David
authors: D
authors: Ruppert
mesh_terms: D000465:Algorithms; D001699:Biometry / Q000379:methods*; D001921:Brain / Q000473:pathology; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D056324:Diffusion Tensor Imaging / Q000706:statistics & numerical data; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D009103:Multiple Sclerosis / Q000473:pathology; D015999:Multivariate Analysis; D016011:Normal Distribution; D012044:Regression Analysis