Modeling longitudinal skewed functional data.

Abstract

This paper introduces a model for longitudinal functional data analysis that accounts for pointwise skewness. The proposed procedure decouples the marginal pointwise variation from the complex longitudinal and functional dependence using copula methodology. Pointwise variation is described through parametric distribution functions that capture varying skewness and change smoothly both in time and over the functional argument. Joint dependence is quantified through a Gaussian copula with a low-rank approximation-based covariance. The introduced class of models provides a unifying platform for both pointwise quantile estimation and prediction of complete trajectories at new times. We investigate the methods numerically in simulations and discuss their application to a diffusion tensor imaging study of multiple sclerosis patients. This approach is implemented in the R package sLFDA that is publicly available on GitHub.