Incorporating covariates in skewed functional data models.

We introduce a class of covariate-adjusted skewed functional models (cSFM) designed for functional data exhibiting location-dependent marginal distributions. We propose a semi-parametric copula model for the pointwise marginal distributions, which are allowed to depend on covariates, and the functional dependence, which is assumed covariate invariant. The proposed cSFM framework provides a unifying platform for pointwise quantile estimation and trajectory prediction. We consider a computationally feasible procedure that handles densely as well as sparsely observed functional data. The methods are examined numerically using simulations and is applied to a new tractography study of multiple sclerosis. Furthermore, the methodology is implemented in the R package cSFM, which is publicly available on CRAN.